Exam 7: Quadratic Equations, Functions and Inequalities

The city of Morgana is 20 miles due west of Vining. Beckett is due north of Morgana. If the distance from Beckett to Vining is 2 miles less than 3 times the distance from Beckett to Morgana, How far apart are Beckett and Morgana? Round to 1 decimal place.

(Multiple Choice)

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Question 41

Solve the inequality. $- x ^ { 2 } - 18 x - 81 < 0$

(Multiple Choice)

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Question 42

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. $f ( x ) = - x ^ { 2 } + 7 x - \frac { 49 } { 4 }$

(Short Answer)

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Question 43

The staging platform for a fireworks display is 8 ft above ground, and the mortars leave the platform at 160 ft/sec. The height of the mortars h(t) (in feet) can be modeled by $h ( t ) = - 16 ( t - 5 ) ^ { 2 } + 408$ where t is the time in seconds after launch. a. If the fuses are set for 5 sec after launch, at what height will the fireworks explode? b. Will the fireworks explode at their maximum height? Explain

(Essay)

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Question 44

Solve for $a . ( a > 0 )$ $a ^ { 2 } + b ^ { 2 } + c ^ { 2 } = d ^ { 2 }$

(Multiple Choice)

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Question 45

The daily profit made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. How many cars must be produced per shift for the company to break even?

(Multiple Choice)

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Question 46

Solve the rational inequality. Write the answer in interval notation. $\frac { ( x + 7 ) ^ { 2 } } { x } > 0$

(Multiple Choice)

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Question 47

Solve the equation. $\frac { 3 z } { z - 3 } + \frac { 3 } { z - 8 } = 1$

(Multiple Choice)

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Question 48

Solve the rational inequality. Write the answer in interval notation. $\frac { 4 g + 4 } { 4 g - 12 } < 0$

(Multiple Choice)

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Question 49

Solve the equation by using substitution. $z ^ { 2 / 3 } + 3 z ^ { 1 / 3 } - 10 = 0$

(Multiple Choice)

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Question 50

The temperature at an Ohio state park for one day in June can be approximated by the function $T ( x ) = 0.284 x ^ { 2 } - 5.11 x + 82 \quad 0 \leq x \leq 18$ where T is degrees Fahrenheit and x is the number of hours after 5 PM on Friday. T(x) has no x-intercepts. Explain why this makes sense in the context of the problem.

(Essay)

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Question 51

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then write the maximum or minimum value. $k ( x ) = \frac { 1 } { 4 } ( x + 3 ) ^ { 2 }$

(Short Answer)

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Question 52

Solve the equation by using the quadratic formula. $- \frac { 4 } { 3 } = \frac { 1 } { 6 } x - 5 x ^ { 2 }$

(Multiple Choice)

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Question 53

Write the function in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ by completing the square. $f ( x ) = x ^ { 2 } + 20 x - 6$

(Multiple Choice)

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Question 54

Find the x-intercepts of the function. $h ( x ) = 16 x ^ { 2 } - 64 x + 64$

(Multiple Choice)

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Question 55

Solve the polynomial inequality. Write the answer in interval notation. $u ^ { 2 } - 12 u \leq - 32$

(Multiple Choice)

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Question 56

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then write the maximum or minimum value. $n ( x ) = - 5 x ^ { 2 } + \frac { 23 } { 3 }$

(Short Answer)

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Question 57

Find the vertex of $g ( x ) = \frac { 1 } { 3 } \left( x + \frac { 24 } { 5 } \right) ^ { 2 } - \frac { 5 } { 24 }$ .

(Multiple Choice)

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Question 58

Graph the function. $f ( x ) = x ^ { 2 } - \frac { 3 } { 2 }$

(Multiple Choice)

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Question 59

Solve the equation by using substitution. $t - 3 \sqrt { t } = - 2$

(Short Answer)

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Question 60

The city of Morgana is 20 miles due west of Vining. Beckett is due north of Morgana. If the distance from Beckett to Vining is 2 miles less than 3 times the distance from Beckett to Morgana, How far apart are Beckett and Morgana? Round to 1 decimal place.

Solve the inequality. $- x ^ { 2 } - 18 x - 81 < 0$

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. $f ( x ) = - x ^ { 2 } + 7 x - \frac { 49 } { 4 }$

Solve for $a . ( a > 0 )$ $a ^ { 2 } + b ^ { 2 } + c ^ { 2 } = d ^ { 2 }$

The daily profit made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. How many cars must be produced per shift for the company to break even?

Solve the rational inequality. Write the answer in interval notation. $\frac { ( x + 7 ) ^ { 2 } } { x } > 0$

Solve the equation. $\frac { 3 z } { z - 3 } + \frac { 3 } { z - 8 } = 1$

Solve the rational inequality. Write the answer in interval notation. $\frac { 4 g + 4 } { 4 g - 12 } < 0$

Solve the equation by using substitution. $z ^ { 2 / 3 } + 3 z ^ { 1 / 3 } - 10 = 0$

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then write the maximum or minimum value. $k ( x ) = \frac { 1 } { 4 } ( x + 3 ) ^ { 2 }$

Solve the equation by using the quadratic formula. $- \frac { 4 } { 3 } = \frac { 1 } { 6 } x - 5 x ^ { 2 }$

Write the function in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ by completing the square. $f ( x ) = x ^ { 2 } + 20 x - 6$

Find the x-intercepts of the function. $h ( x ) = 16 x ^ { 2 } - 64 x + 64$

Solve the polynomial inequality. Write the answer in interval notation. $u ^ { 2 } - 12 u \leq - 32$

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then write the maximum or minimum value. $n ( x ) = - 5 x ^ { 2 } + \frac { 23 } { 3 }$

Find the vertex of $g ( x ) = \frac { 1 } { 3 } \left( x + \frac { 24 } { 5 } \right) ^ { 2 } - \frac { 5 } { 24 }$ .

Graph the function. $f ( x ) = x ^ { 2 } - \frac { 3 } { 2 }$

Solve the equation by using substitution. $t - 3 \sqrt { t } = - 2$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

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Exam 7: Quadratic Equations, Functions and Inequalities

The city of Morgana is 20 miles due west of Vining. Beckett is due north of Morgana. If the distance from Beckett to Vining is 2 miles less than 3 times the distance from Beckett to Morgana, How far apart are Beckett and Morgana? Round to 1 decimal place.

Solve the inequality. −x2−18x−81<0- x ^ { 2 } - 18 x - 81 < 0−x2−18x−81<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. f(x)=−x2+7x−494f ( x ) = - x ^ { 2 } + 7 x - \frac { 49 } { 4 }f(x)=−x2+7x−449​

Solve for a.(a>0)a . ( a > 0 )a.(a>0) a2+b2+c2=d2a ^ { 2 } + b ^ { 2 } + c ^ { 2 } = d ^ { 2 }a2+b2+c2=d2

The daily profit made by an automobile manufacturer is P(x)=−45x2+2,250x−18,000P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000P(x)=−45x2+2,250x−18,000 where x is the number of cars produced per shift. How many cars must be produced per shift for the company to break even?

Solve the rational inequality. Write the answer in interval notation. (x+7)2x>0\frac { ( x + 7 ) ^ { 2 } } { x } > 0x(x+7)2​>0

Solve the equation. 3zz−3+3z−8=1\frac { 3 z } { z - 3 } + \frac { 3 } { z - 8 } = 1z−33z​+z−83​=1

Solve the rational inequality. Write the answer in interval notation. 4g+44g−12<0\frac { 4 g + 4 } { 4 g - 12 } < 04g−124g+4​<0

Solve the equation by using substitution. z2/3+3z1/3−10=0z ^ { 2 / 3 } + 3 z ^ { 1 / 3 } - 10 = 0z2/3+3z1/3−10=0

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then write the maximum or minimum value. k(x)=14(x+3)2k ( x ) = \frac { 1 } { 4 } ( x + 3 ) ^ { 2 }k(x)=41​(x+3)2

Solve the equation by using the quadratic formula. −43=16x−5x2- \frac { 4 } { 3 } = \frac { 1 } { 6 } x - 5 x ^ { 2 }−34​=61​x−5x2

Write the function in the form f(x)=a(x−h)2+kf ( x ) = a ( x - h ) ^ { 2 } + kf(x)=a(x−h)2+k by completing the square. f(x)=x2+20x−6f ( x ) = x ^ { 2 } + 20 x - 6f(x)=x2+20x−6

Find the x-intercepts of the function. h(x)=16x2−64x+64h ( x ) = 16 x ^ { 2 } - 64 x + 64h(x)=16x2−64x+64

Solve the polynomial inequality. Write the answer in interval notation. u2−12u≤−32u ^ { 2 } - 12 u \leq - 32u2−12u≤−32

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then write the maximum or minimum value. n(x)=−5x2+233n ( x ) = - 5 x ^ { 2 } + \frac { 23 } { 3 }n(x)=−5x2+323​

Find the vertex of g(x)=13(x+245)2−524g ( x ) = \frac { 1 } { 3 } \left( x + \frac { 24 } { 5 } \right) ^ { 2 } - \frac { 5 } { 24 }g(x)=31​(x+524​)2−245​ .

Graph the function. f(x)=x2−32f ( x ) = x ^ { 2 } - \frac { 3 } { 2 }f(x)=x2−23​

Solve the equation by using substitution. t−3t=−2t - 3 \sqrt { t } = - 2t−3t​=−2

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Solve the inequality. $- x ^ { 2 } - 18 x - 81 < 0$

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. $f ( x ) = - x ^ { 2 } + 7 x - \frac { 49 } { 4 }$

Solve for $a . ( a > 0 )$ $a ^ { 2 } + b ^ { 2 } + c ^ { 2 } = d ^ { 2 }$

The daily profit made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. How many cars must be produced per shift for the company to break even?

Solve the rational inequality. Write the answer in interval notation. $\frac { ( x + 7 ) ^ { 2 } } { x } > 0$

Solve the equation. $\frac { 3 z } { z - 3 } + \frac { 3 } { z - 8 } = 1$

Solve the rational inequality. Write the answer in interval notation. $\frac { 4 g + 4 } { 4 g - 12 } < 0$

Solve the equation by using substitution. $z ^ { 2 / 3 } + 3 z ^ { 1 / 3 } - 10 = 0$

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then write the maximum or minimum value. $k ( x ) = \frac { 1 } { 4 } ( x + 3 ) ^ { 2 }$

Solve the equation by using the quadratic formula. $- \frac { 4 } { 3 } = \frac { 1 } { 6 } x - 5 x ^ { 2 }$

Write the function in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ by completing the square. $f ( x ) = x ^ { 2 } + 20 x - 6$

Find the x-intercepts of the function. $h ( x ) = 16 x ^ { 2 } - 64 x + 64$

Solve the polynomial inequality. Write the answer in interval notation. $u ^ { 2 } - 12 u \leq - 32$

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then write the maximum or minimum value. $n ( x ) = - 5 x ^ { 2 } + \frac { 23 } { 3 }$

Find the vertex of $g ( x ) = \frac { 1 } { 3 } \left( x + \frac { 24 } { 5 } \right) ^ { 2 } - \frac { 5 } { 24 }$ .

Graph the function. $f ( x ) = x ^ { 2 } - \frac { 3 } { 2 }$

Solve the equation by using substitution. $t - 3 \sqrt { t } = - 2$