Question 1

Solve the equation by using the quadratic formula. $$11 y - 6 + 65 y ^ { 2 } = 0$$

Accepted Answer

A)  $\left\{ \frac { 5 } { 2 } , - \frac { 13 } { 3 } \right\}$ 
B)  $\left\{ \frac { 1 } { 3 } , \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 5 } , \frac { 3 } { 13 } \right\}$ 
D)  $\left\{ \frac { 3 } { 11 } \pm \frac { \sqrt { 4021 } } { 11 } i \right\}$ 
A)  $\left\{ \frac { 5 } { 2 } , - \frac { 13 } { 3 } \right\}$ 
B)  $\left\{ \frac { 1 } { 3 } , \frac { 2 } { 5 } \right\}$ 
C)  $\left\{ - \frac { 2 } { 5 } , \frac { 3 } { 13 } \right\}$ 
D)  $\left\{ \frac { 3 } { 11 } \pm \frac { \sqrt { 4021 } } { 11 } i \right\}$

Question 2

a. Find the vertex.
b. Find the y-intercept.
c. Find the x-intercept(s), if they exist.
d. Use this information to graph the function. 
$g ( x ) = 2 x ^ { 2 } + 12 x + 20$

Accepted Answer

a. (-3, 2)

Question 3

Solve the rational inequality. Write the answer in interval notation. $$\frac { 7 } { x - 3 } \geq 0$$

Accepted Answer

A)  $( - \infty , 3 )$ 
B)  $( - \infty , 3 ]$ 
C)  $[ 3 , \infty )$ 
D)  $( 3 , \infty )$ 
A)  $( - \infty , 3 )$ 
B)  $( - \infty , 3 ]$ 
C)  $[ 3 , \infty )$ 
D)  $( 3 , \infty )$

Question 4

Ramon wants to fence in a rectangular portion of his backyard against the back of his garage for a vegetable garden. He plans to use 40 feet of fence, and needs fence on only three sides. Find the maximum area he can enclose. (Hint: The lengths of the 3 fenced sides of the rectangle must add up to 40.)

Accepted Answer

The answer of Ramon wants to fence in a rectangular...

Question 5

Graph the function. $$h ( x ) = - 2 ( x + 2 ) ^ { 2 } + 6$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Solve the polynomial inequality. Write the answer in interval notation. $$x ^ { 3 } - x ^ { 2 } \leq 56 x$$

Accepted Answer

A)  $( - \infty , - 7 ) \cup ( 0,8 )$ 
B)  $( - 7,8 )$ 
C)  $( - \infty , - 7 ) \cup ( 8 , \infty )$ 
D)  $( - 7,0 ) \cup ( 8 , \infty )$ 
A)  $( - \infty , - 7 ) \cup ( 0,8 )$ 
B)  $( - 7,8 )$ 
C)  $( - \infty , - 7 ) \cup ( 8 , \infty )$ 
D)  $( - 7,0 ) \cup ( 8 , \infty )$

Question 7

Solve the rational inequality. Write the answer in interval notation. $$\frac { 2 t ^ { 2 } + t } { - 4 t + 3 } > 1$$

Accepted Answer

A)  $\left( - \frac { 1 } { 2 } , 0 \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$ 
B)  $\left( - \frac { 3 } { 4 } , - \frac { 1 } { 2 } \right) \cup ( 3 , \infty )$ 
C)  $\left( - 3 , \frac { 1 } { 2 } \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$ 
D)  $( - \infty , - 3 ) \cup \left( \frac { 1 } { 2 } , \frac { 3 } { 4 } \right)$ 
A)  $\left( - \frac { 1 } { 2 } , 0 \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$ 
B)  $\left( - \frac { 3 } { 4 } , - \frac { 1 } { 2 } \right) \cup ( 3 , \infty )$ 
C)  $\left( - 3 , \frac { 1 } { 2 } \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$ 
D)  $( - \infty , - 3 ) \cup \left( \frac { 1 } { 2 } , \frac { 3 } { 4 } \right)$

Question 8

Solve the quadratic equation by completing the square and applying the square root property. $$z ^ { 2 } - \frac { 9 } { 2 } z + 10 = 0$$

Accepted Answer

The answer of Solve the quadratic equation by completing the...

Question 9

Solve the quadratic equation by using any method. $$( m - 18 ) ^ { 2 } - 5 = 0$$

Accepted Answer

The answer of Solve the quadratic equation by using any...

Question 10

Solve the polynomial inequality. Write the answer in interval notation. $$x ^ { 3 } - 3 x ^ { 2 } > 3 - x$$

Accepted Answer

A)  $( - \infty , 3 )$ 
B)  $( - 1,3 )$ 
C)  $( - \infty - 1 ) \cup ( 3 , \infty )$ 
D)  $( 3 , \infty )$ 
A)  $( - \infty , 3 )$ 
B)  $( - 1,3 )$ 
C)  $( - \infty - 1 ) \cup ( 3 , \infty )$ 
D)  $( 3 , \infty )$

Question 11

Solve the inequality. $$x ^ { 4 } + x ^ { 2 } \geq 0$$

Accepted Answer

A)  $( - \infty , 0 ]$ 
B)  {   } 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 1 ] \cup [ 0 , \infty )$ 
A)  $( - \infty , 0 ]$ 
B)  {   } 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 1 ] \cup [ 0 , \infty )$

Question 12

The formula for the area of a circle is $\mathrm { A } = \pi r ^ { 2 }$, where $r$ is the radius. Solve the formula for $r$, and use your answer to find the radius of a circle with area 25 feet. Use $3.14$ for $\pi$ and round the answer to the nearest tenth of a foot.

Accepted Answer

A)  $r = \frac { A } { 2 \pi } ; 4.0$ feet 
B)  $r = \sqrt { A - \pi } ; 4.7$ feet 
C)  $r = \sqrt { \frac { A } { \pi } } , r = - \sqrt { \frac { A } { \pi } } ; 2.8$ feet or $- 2.8$ feet 
D)  $r = \sqrt { \frac { A } { \pi } } ; 2.8$ feet 
A)  $r = \frac { A } { 2 \pi } ; 4.0$ feet 
B)  $r = \sqrt { A - \pi } ; 4.7$ feet 
C)  $r = \sqrt { \frac { A } { \pi } } , r = - \sqrt { \frac { A } { \pi } } ; 2.8$ feet or $- 2.8$ feet 
D)  $r = \sqrt { \frac { A } { \pi } } ; 2.8$ feet

Question 13

Solve the polynomial inequality. Write the answer in interval notation. $$t ( t + 3 ) ( t - 1 ) ^ { 2 } ( t + 1 ) \leq 0$$

Accepted Answer

A)  $[ - 1,1 ]$ 
B)  $[ - 3 , - 1 ] \cup [ 0 , \infty )$ 
C)  $( - \infty , - 3 ] \cup [ - 1,0 ] \cup \{ 1 \}$ 
D)  $( - \infty , - 3 ] \cup [ - 1,0 ] \cup [ 1 , \infty )$ 
A)  $[ - 1,1 ]$ 
B)  $[ - 3 , - 1 ] \cup [ 0 , \infty )$ 
C)  $( - \infty , - 3 ] \cup [ - 1,0 ] \cup \{ 1 \}$ 
D)  $( - \infty , - 3 ] \cup [ - 1,0 ] \cup [ 1 , \infty )$

Question 14

Solve the equation by using substitution. $$x - 6 = \sqrt { x }$$

Accepted Answer

The answer of Solve the equation by using substitution. \[x...

Question 15

a. Factor the expression $2 x ^ { 3 } - 24 x ^ { 2 } + 144 x$ 
b. Use the zero product rule and the quadratic formula to solve the equation $2 x ^ { 3 } - 24 x ^ { 2 } + 144 x = 0 .$ There should be three solutions.

Accepted Answer

The answer of a. Factor the expression \(2 x ^...

Question 16

Solve the quadratic equation by completing the square and applying the square root property. $$3 x ^ { 2 } - 12 x + 21 = 0$$

Accepted Answer

A)  $\{ 2 + \sqrt { 3 } , 2 - \sqrt { 3 } \}$ 
B)  $\{ 2 + i \sqrt { 3 } , 2 - i \sqrt { 3 } \}$ 
C)  $\left\{ \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right\}$ 
D)  $\{ - 2 + i \sqrt { 5 } , - 2 - i \sqrt { 5 } \}$ 
A)  $\{ 2 + \sqrt { 3 } , 2 - \sqrt { 3 } \}$ 
B)  $\{ 2 + i \sqrt { 3 } , 2 - i \sqrt { 3 } \}$ 
C)  $\left\{ \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right\}$ 
D)  $\{ - 2 + i \sqrt { 5 } , - 2 - i \sqrt { 5 } \}$

Question 17

If we ignore air resistance, the distance d(t) (in feet) that an object travels in free fall can be approximated by $d ( t ) = 16 t ^ { 2 }$ , where t is the time in seconds after the object was dropped. If a Building is 1323 ft high, how long will it take an object to fall from the top of the building? Round To one decimal place.

Accepted Answer

A)  9.1 sec 
B)  2.3 sec 
C)  36.4 sec 
D)  12.9 sec 
A)  9.1 sec 
B)  2.3 sec 
C)  36.4 sec 
D)  12.9 sec

Question 18

Solve the quadratic equation by using any method. $$\frac { 19 } { 4 } x ^ { 2 } + 14 x = \frac { 3 } { 4 }$$

Accepted Answer

The answer of Solve the quadratic equation by using any...

Question 19

Write the equation of the axis of symmetry of the parabola. $$f ( x ) = - 20 ( x + 6 ) ^ { 2 } + 5$$

Accepted Answer

A)  x = -6 
B)  x = 6 
C)  y = 5 
D)  x = 5 
A)  x = -6 
B)  x = 6 
C)  y = 5 
D)  x = 5

Question 20

Solve the equation by using substitution. $$3 \left( t ^ { 2 } - 25 \right) ^ { 2 } + 16 \left( t ^ { 2 } - 25 \right) = - 5$$

Accepted Answer

The answer of Solve the equation by using substitution. \[3...

Solve the equation by using the quadratic formula. $11 y - 6 + 65 y ^ { 2 } = 0$

a. Find the vertex. b. Find the y-intercept. c. Find the x-intercept(s), if they exist. d. Use this information to graph the function. $g ( x ) = 2 x ^ { 2 } + 12 x + 20$

Solve the rational inequality. Write the answer in interval notation. $\frac { 7 } { x - 3 } \geq 0$

Graph the function. $h ( x ) = - 2 ( x + 2 ) ^ { 2 } + 6$

Solve the polynomial inequality. Write the answer in interval notation. $x ^ { 3 } - x ^ { 2 } \leq 56 x$

Solve the rational inequality. Write the answer in interval notation. $\frac { 2 t ^ { 2 } + t } { - 4 t + 3 } > 1$

Solve the quadratic equation by completing the square and applying the square root property. $z ^ { 2 } - \frac { 9 } { 2 } z + 10 = 0$

Solve the quadratic equation by using any method. $( m - 18 ) ^ { 2 } - 5 = 0$

Solve the polynomial inequality. Write the answer in interval notation. $x ^ { 3 } - 3 x ^ { 2 } > 3 - x$

Solve the inequality. $x ^ { 4 } + x ^ { 2 } \geq 0$

The formula for the area of a circle is $\mathrm { A } = \pi r ^ { 2 }$ , where $r$ is the radius. Solve the formula for $r$ , and use your answer to find the radius of a circle with area 25 feet. Use $3.14$ for $\pi$ and round the answer to the nearest tenth of a foot.

Solve the polynomial inequality. Write the answer in interval notation. $t ( t + 3 ) ( t - 1 ) ^ { 2 } ( t + 1 ) \leq 0$

Solve the equation by using substitution. $x - 6 = \sqrt { x }$

a. Factor the expression $2 x ^ { 3 } - 24 x ^ { 2 } + 144 x$ b. Use the zero product rule and the quadratic formula to solve the equation $2 x ^ { 3 } - 24 x ^ { 2 } + 144 x = 0 .$ There should be three solutions.

Solve the quadratic equation by completing the square and applying the square root property. $3 x ^ { 2 } - 12 x + 21 = 0$

Solve the quadratic equation by using any method. $\frac { 19 } { 4 } x ^ { 2 } + 14 x = \frac { 3 } { 4 }$

Write the equation of the axis of symmetry of the parabola. $f ( x ) = - 20 ( x + 6 ) ^ { 2 } + 5$

Solve the equation by using substitution. $3 \left( t ^ { 2 } - 25 \right) ^ { 2 } + 16 \left( t ^ { 2 } - 25 \right) = - 5$

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Exam 7: Quadratic Equations, Functions and Inequalities

Solve the equation by using the quadratic formula. 11y−6+65y2=011 y - 6 + 65 y ^ { 2 } = 011y−6+65y2=0

a. Find the vertex. b. Find the y-intercept. c. Find the x-intercept(s), if they exist. d. Use this information to graph the function. g(x)=2x2+12x+20g ( x ) = 2 x ^ { 2 } + 12 x + 20g(x)=2x2+12x+20

Solve the rational inequality. Write the answer in interval notation. 7x−3≥0\frac { 7 } { x - 3 } \geq 0x−37​≥0

Graph the function. h(x)=−2(x+2)2+6h ( x ) = - 2 ( x + 2 ) ^ { 2 } + 6h(x)=−2(x+2)2+6

Solve the polynomial inequality. Write the answer in interval notation. x3−x2≤56xx ^ { 3 } - x ^ { 2 } \leq 56 xx3−x2≤56x

Solve the rational inequality. Write the answer in interval notation. 2t2+t−4t+3>1\frac { 2 t ^ { 2 } + t } { - 4 t + 3 } > 1−4t+32t2+t​>1

Solve the quadratic equation by completing the square and applying the square root property. z2−92z+10=0z ^ { 2 } - \frac { 9 } { 2 } z + 10 = 0z2−29​z+10=0

Solve the quadratic equation by using any method. (m−18)2−5=0( m - 18 ) ^ { 2 } - 5 = 0(m−18)2−5=0

Solve the polynomial inequality. Write the answer in interval notation. x3−3x2>3−xx ^ { 3 } - 3 x ^ { 2 } > 3 - xx3−3x2>3−x

Solve the inequality. x4+x2≥0x ^ { 4 } + x ^ { 2 } \geq 0x4+x2≥0

The formula for the area of a circle is A=πr2\mathrm { A } = \pi r ^ { 2 }A=πr2 , where rrr is the radius. Solve the formula for rrr , and use your answer to find the radius of a circle with area 25 feet. Use 3.143.143.14 for π\piπ and round the answer to the nearest tenth of a foot.

Solve the polynomial inequality. Write the answer in interval notation. t(t+3)(t−1)2(t+1)≤0t ( t + 3 ) ( t - 1 ) ^ { 2 } ( t + 1 ) \leq 0t(t+3)(t−1)2(t+1)≤0

Solve the equation by using substitution. x−6=xx - 6 = \sqrt { x }x−6=x​

a. Factor the expression 2x3−24x2+144x2 x ^ { 3 } - 24 x ^ { 2 } + 144 x2x3−24x2+144x b. Use the zero product rule and the quadratic formula to solve the equation 2x3−24x2+144x=0.2 x ^ { 3 } - 24 x ^ { 2 } + 144 x = 0 .2x3−24x2+144x=0. There should be three solutions.

Solve the quadratic equation by completing the square and applying the square root property. 3x2−12x+21=03 x ^ { 2 } - 12 x + 21 = 03x2−12x+21=0

Solve the quadratic equation by using any method. 194x2+14x=34\frac { 19 } { 4 } x ^ { 2 } + 14 x = \frac { 3 } { 4 }419​x2+14x=43​

Write the equation of the axis of symmetry of the parabola. f(x)=−20(x+6)2+5f ( x ) = - 20 ( x + 6 ) ^ { 2 } + 5f(x)=−20(x+6)2+5

Solve the equation by using substitution. 3(t2−25)2+16(t2−25)=−53 \left( t ^ { 2 } - 25 \right) ^ { 2 } + 16 \left( t ^ { 2 } - 25 \right) = - 53(t2−25)2+16(t2−25)=−5