Question 1

Find the vertex and focus of the parabola. $x ^ { 2 } + 12 y = 0$

Accepted Answer

A) vertex: (0,0)focus: $( 0 , - 3 )$ 
B) vertex: (0,0)focus: $( 0,3 )$ 
C) vertex: $$( 3,0 )$$ focus: (0,0) 
D) vertex: $$( - 3,0 )$$ focus: (0,0) 
E) vertex: (0,0)focus: $( 3,0 )$ 
A) vertex: (0,0)focus: $( 0 , - 3 )$ 
B) vertex: (0,0)focus: $( 0,3 )$ 
C) vertex: $$( 3,0 )$$ focus: (0,0) 
D) vertex: $$( - 3,0 )$$ focus: (0,0) 
E) vertex: (0,0)focus: $( 3,0 )$

Question 2

Find the center and the vertices which located on the major axis of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

Accepted Answer

A) center: (0,0)vertices: (-9,0), (9,0) 
B) center: (0,0)vertices: (0,-9), (0,9) 
C) center: (-9,9)vertices: (-1,0), (1,0) 
D) center: (0,0)vertices: (-9,-1), (9,1) 
E) center: (-9,9)vertices: (-1,-9), (1,9) 
A) center: (0,0)vertices: (-9,0), (9,0) 
B) center: (0,0)vertices: (0,-9), (0,9) 
C) center: (-9,9)vertices: (-1,0), (1,0) 
D) center: (0,0)vertices: (-9,-1), (9,1) 
E) center: (-9,9)vertices: (-1,-9), (1,9)

Question 3

Write the equation of the circle graphed below.Express the equation in standard form.​

Accepted Answer

The answer of Write the equation of the circle graphed...

Question 4

The revenue R (in dollars)generated by the sale of x units of a digital camera is given by $( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )$ .Approximate the number of sales that will maximize revenue. ​

Accepted Answer

A) Maximum revenue occurs at $x = 4,205$ units. 
B) Maximum revenue occurs at $$x = 406$$ units. 
C) Maximum revenue occurs at $x = 145$ units. 
D) Maximum revenue occurs at $x = 29,435$ units. 
E) Maximum revenue occurs at $x = 21,025$ units. 
A) Maximum revenue occurs at $x = 4,205$ units. 
B) Maximum revenue occurs at $$x = 406$$ units. 
C) Maximum revenue occurs at $x = 145$ units. 
D) Maximum revenue occurs at $x = 29,435$ units. 
E) Maximum revenue occurs at $x = 21,025$ units.

Question 5

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$ ​

Accepted Answer

A)  $y ^ { 2 } = - \frac { 28 } { 2 } x$ 
B)  $x ^ { 2 } = \frac { 2 } { 28 } y$ 
C)  $y ^ { 2 } = - \frac { 2 } { 28 } x$ 
D)  $x ^ { 2 } = - \frac { 2 } { 28 } y$ 
E)  $y ^ { 2 } = \frac { 2 } { 28 } x$ 
A)  $y ^ { 2 } = - \frac { 28 } { 2 } x$ 
B)  $x ^ { 2 } = \frac { 2 } { 28 } y$ 
C)  $y ^ { 2 } = - \frac { 2 } { 28 } x$ 
D)  $x ^ { 2 } = - \frac { 2 } { 28 } y$ 
E)  $y ^ { 2 } = \frac { 2 } { 28 } x$

Question 6

Find the equation of the parabola with vertex at (0,0)and focus at (0,6).Express the equation in standard form.

Accepted Answer

The answer of Find the equation of the parabola with...

Question 7

Roads are often designed with parabolic surfaces to allow rain to drain off.A particular road that is 44 feet wide is 0.4 foot higher in the center than it is on the sides (see figure).​   ​ where $a = 44$ ft, $b = 0.4 \mathrm { ft }$ ​
Find an equation of the parabola that models the road surface.(Assume that the origin is at the center of the road. )
​

Accepted Answer

A)  $x ^ { 2 } = - 1210 y \text { or } y = - \frac { 1 } { 1210 } x ^ { 2 }$ 
B)  $y ^ { 2 } = - 1210 x \text { or } x = - \frac { 1 } { 1210 } y ^ { 2 }$ 
C)  $x ^ { 2 } = 1210 y \text { or } y = \frac { 1 } { 1210 } x ^ { 2 }$ 
D)  $y ^ { 2 } = 1210 \mathrm { x } \text { or } x = \frac { 1 } { 1210 } y ^ { 2 }$ 
E)  $x ^ { 2 } = 44 y \text { or } y = \frac { 1 } { 44 } x ^ { 2 }$ 
A)  $x ^ { 2 } = - 1210 y \text { or } y = - \frac { 1 } { 1210 } x ^ { 2 }$ 
B)  $y ^ { 2 } = - 1210 x \text { or } x = - \frac { 1 } { 1210 } y ^ { 2 }$ 
C)  $x ^ { 2 } = 1210 y \text { or } y = \frac { 1 } { 1210 } x ^ { 2 }$ 
D)  $y ^ { 2 } = 1210 \mathrm { x } \text { or } x = \frac { 1 } { 1210 } y ^ { 2 }$ 
E)  $x ^ { 2 } = 44 y \text { or } y = \frac { 1 } { 44 } x ^ { 2 }$

Question 8

Give the coordinates of the circle's center and it radius.​ $$( x - 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 16$$ ​
Enter your answer using the coordinate notation: (a,b),and r = ....separated with a comma.

Accepted Answer

The answer of Give the coordinates of the circle's center...

Question 9

Select the standard form of the equation of the parabola and determine the coordinates of the focus.​   ​

Accepted Answer

A)  $x ^ { 2 } = \frac { 5 } { 2 } y$ ;Focus: $\left( 0 , \frac { 5 } { 8 } \right)$ 
B)  $y ^ { 2 } = - \frac { 5 } { 2 } x$ ;Focus: $\left( - \frac { 5 } { 8 } , 0 \right)$ 
C)  $x ^ { 2 } = - \frac { 5 } { 2 } y$ ;Focus: $$\left( 0 , - \frac { 5 } { 8 } \right)$$ 
D)  $y ^ { 2 } = \frac { 5 } { 2 } x$ ;Focus: $\left( \frac { 5 } { 8 } , 0 \right)$ 
E)  $y ^ { 2 } = \frac { 5 } { 2 } x$ ;Focus: $( 5,0 )$ 
A)  $x ^ { 2 } = \frac { 5 } { 2 } y$ ;Focus: $\left( 0 , \frac { 5 } { 8 } \right)$ 
B)  $y ^ { 2 } = - \frac { 5 } { 2 } x$ ;Focus: $\left( - \frac { 5 } { 8 } , 0 \right)$ 
C)  $x ^ { 2 } = - \frac { 5 } { 2 } y$ ;Focus: $$\left( 0 , - \frac { 5 } { 8 } \right)$$ 
D)  $y ^ { 2 } = \frac { 5 } { 2 } x$ ;Focus: $\left( \frac { 5 } { 8 } , 0 \right)$ 
E)  $y ^ { 2 } = \frac { 5 } { 2 } x$ ;Focus: $( 5,0 )$

Question 10

Graph the following equation.​ $$x ^ { 2 } - 6 x + y ^ { 2 } = 7$$ ​

Accepted Answer

A) ​   
B) ​   
C) ​   
A) ​   
B) ​   
C) ​

Question 11

Find the vertex and focus of the parabola for the given equation and select its graph.​ $$y ^ { 2 } = - 4 x$$ ​

Accepted Answer

A) Vertex: (0,0) Focus: (1,0)   
B) Vertex: (0,0) Focus: (1,0)   
C) Vertex: (0,0) Focus: (-1,0)   
D) Vertex: (0,0) Focus: ( - 1,0)   
E) Vertex: (0,0) Focus: (0,1)   
A) Vertex: (0,0) Focus: (1,0)   
B) Vertex: (0,0) Focus: (1,0)   
C) Vertex: (0,0) Focus: (-1,0)   
D) Vertex: (0,0) Focus: ( - 1,0)   
E) Vertex: (0,0) Focus: (0,1)

Question 12

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Passes through the point (2,4);horizontal axis
​

Accepted Answer

A)  $x ^ { 2 } = 8 y$ 
B)  $x ^ { 2 } = - 8 y$ 
C)  $y ^ { 2 } = 8 x$ 
D)  $y ^ { 2 } = - 8 x$ 
E)  $y ^ { 2 } = \frac { x } { 8 }$ 
A)  $x ^ { 2 } = 8 y$ 
B)  $x ^ { 2 } = - 8 y$ 
C)  $y ^ { 2 } = 8 x$ 
D)  $y ^ { 2 } = - 8 x$ 
E)  $y ^ { 2 } = \frac { x } { 8 }$

Question 13

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure).   L = 5 inches ​
Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Accepted Answer

A) ​ $$y = \frac { 1 } { 5 } x ^ { 2 }$$ ​ 
B)  $y = 5 x ^ { 2 }$ 
C)  $y = 20 x ^ { 2 }$ ​ 
D)  $x ^ { 2 } = 20 y$ 
E)  $$x ^ { 2 } = 5 y$$ 
A) ​ $$y = \frac { 1 } { 5 } x ^ { 2 }$$ ​ 
B)  $y = 5 x ^ { 2 }$ 
C)  $y = 20 x ^ { 2 }$ ​ 
D)  $x ^ { 2 } = 20 y$ 
E)  $$x ^ { 2 } = 5 y$$

Question 14

Give the standard form of the equation of the parabola with the given characteristics. focus: (-3,13)directrix: $y = 3$

Accepted Answer

A)  $( y - 8 ) ^ { 2 } = - 20 ( x + 3 )$ 
B)  $( x - 8 ) ^ { 2 } = - 20 ( y + 3 )$ 
C)  $( y + 8 ) ^ { 2 } = - 20 ( x - 3 )$ 
D)  $( x + 3 ) ^ { 2 } = 20 ( y - 8 )$ 
E)  $( x - 3 ) ^ { 2 } = 20 ( y + 8 )$ 
A)  $( y - 8 ) ^ { 2 } = - 20 ( x + 3 )$ 
B)  $( x - 8 ) ^ { 2 } = - 20 ( y + 3 )$ 
C)  $( y + 8 ) ^ { 2 } = - 20 ( x - 3 )$ 
D)  $( x + 3 ) ^ { 2 } = 20 ( y - 8 )$ 
E)  $( x - 3 ) ^ { 2 } = 20 ( y + 8 )$

Question 15

Find the vertex and focus of the parabola. $x ^ { 2 } + 28 y = 0$

Accepted Answer

A) vertex: (-7 ,0)focus: (0,0) 
B) vertex: (7,0)focus: (0,0) 
C) vertex: (0,0)focus: (-7,0) 
D) vertex: (0,0)focus: (0,-7) 
E) vertex: (0,0)focus: (0,7) 
A) vertex: (-7 ,0)focus: (0,0) 
B) vertex: (7,0)focus: (0,0) 
C) vertex: (0,0)focus: (-7,0) 
D) vertex: (0,0)focus: (0,-7) 
E) vertex: (0,0)focus: (0,7)

Question 16

A solar oven uses a parabolic reflector to focus the sun's rays at a point 7 inches from the vertex of the reflector (see figure).   L = 7 inches ​
Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Accepted Answer

A)  $y = 28 x ^ { 2 }$ 
B)  $y = \frac { 1 } { 7 } x ^ { 2 }$ 
C)  $x ^ { 2 } = 28 y$ 
D)  $y ^ { 2 } = 7 x$ 
E)  $x ^ { 2 } = 7 y$ 
A)  $y = 28 x ^ { 2 }$ 
B)  $y = \frac { 1 } { 7 } x ^ { 2 }$ 
C)  $x ^ { 2 } = 28 y$ 
D)  $y ^ { 2 } = 7 x$ 
E)  $x ^ { 2 } = 7 y$

Question 17

Identify the conic.​ $4 y ^ { 2 } - 3 x ^ { 2 } + 12 = 0$ ​

Accepted Answer

A) Circle 
B) Ellipse 
C) Hyperbola 
D) Parabola 
E) Line 
A) Circle 
B) Ellipse 
C) Hyperbola 
D) Parabola 
E) Line

Question 18

Use a graphing utility to graph the parabola. $$x + 4 = 8 ( y - 5 ) ^ { 2 }$$

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 19

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​
Directrix: $x = - 6$ ​

Accepted Answer

A)  $y ^ { 2 } = 24 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = - 24 x$ 
D)  $x ^ { 2 } = 24 y$ 
E)  $x ^ { 2 } = - 24 y$ 
A)  $y ^ { 2 } = 24 x$ 
B)  $y ^ { 2 } = x$ 
C)  $y ^ { 2 } = - 24 x$ 
D)  $x ^ { 2 } = 24 y$ 
E)  $x ^ { 2 } = - 24 y$

Question 20

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​
Directrix: x = 3
​

Accepted Answer

A)  $x ^ { 2 } = - 12 y$ 
B)  $y ^ { 2 } = 12 x$ 
C)  $y ^ { 2 } = \frac { x } { 12 }$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $y ^ { 2 } = - 12 x$ 
A)  $x ^ { 2 } = - 12 y$ 
B)  $y ^ { 2 } = 12 x$ 
C)  $y ^ { 2 } = \frac { x } { 12 }$ 
D)  $x ^ { 2 } = 12 y$ 
E)  $y ^ { 2 } = - 12 x$

Exam 60: Introduction to Conics Parabolas

Find the vertex and focus of the parabola. x2+12y=0x ^ { 2 } + 12 y = 0x2+12y=0

Find the center and the vertices which located on the major axis of the ellipse. 81x2+y2=8181 x ^ { 2 } + y ^ { 2 } = 8181x2+y2=81

Write the equation of the circle graphed below.Express the equation in standard form.​

The revenue R (in dollars)generated by the sale of x units of a digital camera is given by (x−145)2=−57(R−29,435)( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )(x−145)2=−75​(R−29,435) .Approximate the number of sales that will maximize revenue. ​

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: (−72,0)\left( - \frac { 7 } { 2 } , 0 \right)(−27​,0) ​

Find the equation of the parabola with vertex at (0,0)and focus at (0,6).Express the equation in standard form.

Give the coordinates of the circle's center and it radius.​ (x−7)2+(y+8)2=16( x - 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 16(x−7)2+(y+8)2=16 ​ Enter your answer using the coordinate notation: (a,b),and r = ....separated with a comma.

Select the standard form of the equation of the parabola and determine the coordinates of the focus.​ ​

Graph the following equation.​ x2−6x+y2=7x ^ { 2 } - 6 x + y ^ { 2 } = 7x2−6x+y2=7 ​

Find the vertex and focus of the parabola for the given equation and select its graph.​ y2=−4xy ^ { 2 } = - 4 xy2=−4x ​

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​ Passes through the point (2,4);horizontal axis ​

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure). L = 5 inches ​ Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Give the standard form of the equation of the parabola with the given characteristics. focus: (-3,13)directrix: y=3y = 3y=3

Find the vertex and focus of the parabola. x2+28y=0x ^ { 2 } + 28 y = 0x2+28y=0

A solar oven uses a parabolic reflector to focus the sun's rays at a point 7 inches from the vertex of the reflector (see figure). L = 7 inches ​ Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Identify the conic.​ 4y2−3x2+12=04 y ^ { 2 } - 3 x ^ { 2 } + 12 = 04y2−3x2+12=0 ​

Use a graphing utility to graph the parabola. x+4=8(y−5)2x + 4 = 8 ( y - 5 ) ^ { 2 }x+4=8(y−5)2

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. ​ Directrix: x=−6x = - 6x=−6 ​

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. ​ Directrix: x = 3 ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Ellipses

Find the vertex and focus of the parabola. $x ^ { 2 } + 12 y = 0$

Find the center and the vertices which located on the major axis of the ellipse. $81 x ^ { 2 } + y ^ { 2 } = 81$

Write the equation of the circle graphed below.Express the equation in standard form.

The revenue R (in dollars)generated by the sale of x units of a digital camera is given by $( x - 145 ) ^ { 2 } = - \frac { 5 } { 7 } ( R - 29,435 )$ .Approximate the number of sales that will maximize revenue.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Focus: $\left( - \frac { 7 } { 2 } , 0 \right)$

Give the coordinates of the circle's center and it radius. $( x - 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 16$ Enter your answer using the coordinate notation: (a,b),and r = ....separated with a comma.

Select the standard form of the equation of the parabola and determine the coordinates of the focus.

Graph the following equation. $x ^ { 2 } - 6 x + y ^ { 2 } = 7$

Find the vertex and focus of the parabola for the given equation and select its graph. $y ^ { 2 } = - 4 x$

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. Passes through the point (2,4);horizontal axis

A solar oven uses a parabolic reflector to focus the sun's rays at a point 5 inches from the vertex of the reflector (see figure). L = 5 inches Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Give the standard form of the equation of the parabola with the given characteristics. focus: (-3,13)directrix: $y = 3$

Find the vertex and focus of the parabola. $x ^ { 2 } + 28 y = 0$

A solar oven uses a parabolic reflector to focus the sun's rays at a point 7 inches from the vertex of the reflector (see figure). L = 7 inches Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin.

Identify the conic. $4 y ^ { 2 } - 3 x ^ { 2 } + 12 = 0$

Use a graphing utility to graph the parabola. $x + 4 = 8 ( y - 5 ) ^ { 2 }$

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. Directrix: $x = - 6$

Find the standard form of the equation of the parabola with the given characteristic(s)and vertex at the origin. Directrix: x = 3