Exam 9: Quadratic Equations, Inequalities, and Functions

Solve the problem using Galileo's formula, $d=16 t^{2}$ . Round your answer to the nearest tenth. -A young boy is delighted to drop various objects from a hotel balcony to the ground below. If he is $161 \mathrm{ft}$ above the ground, how long does it take for one of the objects to fall to the ground?

(Multiple Choice)

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Question 61

Use the graph of a quadratic function to find the solution set of the equation or inequality. - $x^{2}+10 x+24 \geq 0$ $Use the graph of a quadratic function to find the solution set of the equation or inequality. - x^{2}+10 x+24 \geq 0$

(Multiple Choice)

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Question 62

$f(x)=-4 x^{2}+10 x+3$

(Multiple Choice)

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Question 63

Solve by any method. - $16 \mathrm{x}^{4}-41 \mathrm{x}^{2}+25=0$

(Multiple Choice)

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Question 64

Use the square root property to solve the equation. - $(x+9)^{2}-6=0$

(Multiple Choice)

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Question 65

Identify the vertex of the given parabola. - $f(x)=\frac{1}{7} x^{2}$

(Multiple Choice)

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Question 66

Solve the equation by using the square root property or completing the square. - $(5 \mathrm{~s}+7)^{2}=25$

(Multiple Choice)

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Question 67

True or false? The equation $(x+18)^{2}=0$ has exactly one real solution. If false, give the correct number of real solutions.

(Multiple Choice)

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Question 68

Find the vertex of the parabola - $f(x)=4 x^{2}-40 x+101$

(Multiple Choice)

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Question 69

Graph the parabola. - $x=(y-4)^{2}-6$ $Graph the parabola. - x=(y-4)^{2}-6$

(Multiple Choice)

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Question 70

Choose the one alternative that best completes the statement or answers the question. -If it takes y hours to read a book, what is the worker's rate (in jobs per hour)?

(Multiple Choice)

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Question 71

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers. - $25 x^{2}=64 a$

(Multiple Choice)

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Question 72

Solve the inequality, and graph the solution set. - $\frac{x-9}{x+3}>0$ $Solve the inequality, and graph the solution set. - \frac{x-9}{x+3}>0$

(Multiple Choice)

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Question 73

Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate. -A rug is to fit in a room so that a border of even width is left on all four sides. If the room is $12 \mathrm{ft}$ by $15 \mathrm{ft}$ and the area of the rug is $108 \mathrm{ft}^{2}$ , how wide will the border be?

(Multiple Choice)

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Question 74

Choose the one alternative that best completes the statement or answers the question. - $Choose the one alternative that best completes the statement or answers the question. - Using only this graph of f(x)=a(x-h)^{2}+k , what are the signs of h and k ?$ Using only this graph of $f(x)=a(x-h)^{2}+k$ , what are the signs of $h$ and $k$ ?

(Multiple Choice)

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Question 75

Which of the four methods of solving quadratic equations work for any quadratic equation?

(Short Answer)

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Question 76

Solve the equation. - $\sqrt{x+3}=x-3$

(Multiple Choice)

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Question 77

Use the equation $5 x^{2}+6 x=c$ to explain how to solve a quadratic equation by completing the square.

(Essay)

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Question 78

Graph the parabola. - $x=y^{2}+3 y+2$ $Graph the parabola. - x=y^{2}+3 y+2$

(Multiple Choice)

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Question 79

Use the quadratic formula to solve the equation. - $0.7 x^{2}+0.3 x+0.5=0$

(Multiple Choice)

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Question 80

Showing 61 - 80 of 339

Use the graph of a quadratic function to find the solution set of the equation or inequality. - $x^{2}+10 x+24 \geq 0$ $Use the graph of a quadratic function to find the solution set of the equation or inequality. - x^{2}+10 x+24 \geq 0$

$f(x)=-4 x^{2}+10 x+3$

Solve by any method. - $16 \mathrm{x}^{4}-41 \mathrm{x}^{2}+25=0$

Use the square root property to solve the equation. - $(x+9)^{2}-6=0$

Identify the vertex of the given parabola. - $f(x)=\frac{1}{7} x^{2}$

Solve the equation by using the square root property or completing the square. - $(5 \mathrm{~s}+7)^{2}=25$

True or false? The equation $(x+18)^{2}=0$ has exactly one real solution. If false, give the correct number of real solutions.

Find the vertex of the parabola - $f(x)=4 x^{2}-40 x+101$

Graph the parabola. - $x=(y-4)^{2}-6$ $Graph the parabola. - x=(y-4)^{2}-6$

Choose the one alternative that best completes the statement or answers the question. -If it takes y hours to read a book, what is the worker's rate (in jobs per hour)?

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers. - $25 x^{2}=64 a$

Solve the inequality, and graph the solution set. - $\frac{x-9}{x+3}>0$ $Solve the inequality, and graph the solution set. - \frac{x-9}{x+3}>0$

Which of the four methods of solving quadratic equations work for any quadratic equation?

Solve the equation. - $\sqrt{x+3}=x-3$

Use the equation $5 x^{2}+6 x=c$ to explain how to solve a quadratic equation by completing the square.

Graph the parabola. - $x=y^{2}+3 y+2$ $Graph the parabola. - x=y^{2}+3 y+2$

Use the quadratic formula to solve the equation. - $0.7 x^{2}+0.3 x+0.5=0$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Exam 9: Quadratic Equations, Inequalities, and Functions

Use the graph of a quadratic function to find the solution set of the equation or inequality. - x2+10x+24≥0x^{2}+10 x+24 \geq 0x2+10x+24≥0

f(x)=−4x2+10x+3f(x)=-4 x^{2}+10 x+3f(x)=−4x2+10x+3

Solve by any method. - 16x4−41x2+25=016 \mathrm{x}^{4}-41 \mathrm{x}^{2}+25=016x4−41x2+25=0

Use the square root property to solve the equation. - (x+9)2−6=0(x+9)^{2}-6=0(x+9)2−6=0

Identify the vertex of the given parabola. - f(x)=17x2f(x)=\frac{1}{7} x^{2}f(x)=71​x2

Solve the equation by using the square root property or completing the square. - (5 s+7)2=25(5 \mathrm{~s}+7)^{2}=25(5 s+7)2=25

True or false? The equation (x+18)2=0(x+18)^{2}=0(x+18)2=0 has exactly one real solution. If false, give the correct number of real solutions.

Find the vertex of the parabola - f(x)=4x2−40x+101f(x)=4 x^{2}-40 x+101f(x)=4x2−40x+101

Graph the parabola. - x=(y−4)2−6x=(y-4)^{2}-6x=(y−4)2−6

Choose the one alternative that best completes the statement or answers the question. -If it takes y hours to read a book, what is the worker's rate (in jobs per hour)?

Solve for xxx . Assume that aaa and bbb represent positive real numbers. - 25x2=64a25 x^{2}=64 a25x2=64a

Solve the inequality, and graph the solution set. - x−9x+3>0\frac{x-9}{x+3}>0x+3x−9​>0

Choose the one alternative that best completes the statement or answers the question. - Using only this graph of f(x)=a(x−h)2+kf(x)=a(x-h)^{2}+kf(x)=a(x−h)2+k , what are the signs of hhh and kkk ?

Which of the four methods of solving quadratic equations work for any quadratic equation?

Solve the equation. - x+3=x−3\sqrt{x+3}=x-3x+3​=x−3

Use the equation 5x2+6x=c5 x^{2}+6 x=c5x2+6x=c to explain how to solve a quadratic equation by completing the square.

Graph the parabola. - x=y2+3y+2x=y^{2}+3 y+2x=y2+3y+2

Use the quadratic formula to solve the equation. - 0.7x2+0.3x+0.5=00.7 x^{2}+0.3 x+0.5=00.7x2+0.3x+0.5=0

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Nonlinear Functions, Conic Sections, and Nonlinear Systems

Further Topics in Algebra

Appendices

Filters

Use the graph of a quadratic function to find the solution set of the equation or inequality. - $x^{2}+10 x+24 \geq 0$ $Use the graph of a quadratic function to find the solution set of the equation or inequality. - x^{2}+10 x+24 \geq 0$

$f(x)=-4 x^{2}+10 x+3$

Solve by any method. - $16 \mathrm{x}^{4}-41 \mathrm{x}^{2}+25=0$

Use the square root property to solve the equation. - $(x+9)^{2}-6=0$

Identify the vertex of the given parabola. - $f(x)=\frac{1}{7} x^{2}$

Solve the equation by using the square root property or completing the square. - $(5 \mathrm{~s}+7)^{2}=25$

True or false? The equation $(x+18)^{2}=0$ has exactly one real solution. If false, give the correct number of real solutions.

Find the vertex of the parabola - $f(x)=4 x^{2}-40 x+101$

Graph the parabola. - $x=(y-4)^{2}-6$ $Graph the parabola. - x=(y-4)^{2}-6$

Solve for $x$ . Assume that $a$ and $b$ represent positive real numbers. - $25 x^{2}=64 a$

Solve the inequality, and graph the solution set. - $\frac{x-9}{x+3}>0$ $Solve the inequality, and graph the solution set. - \frac{x-9}{x+3}>0$

Solve the equation. - $\sqrt{x+3}=x-3$

Use the equation $5 x^{2}+6 x=c$ to explain how to solve a quadratic equation by completing the square.

Graph the parabola. - $x=y^{2}+3 y+2$ $Graph the parabola. - x=y^{2}+3 y+2$

Use the quadratic formula to solve the equation. - $0.7 x^{2}+0.3 x+0.5=0$