Question 1

A gardener is fencing off a rectangular area with a fixed perimeter of $72 \mathrm{ft}$. What is the maximum area?

Accepted Answer

A)  $18 \mathrm{ft}^{2}$ 
B)  $1296 \mathrm{ft}^{2}$ 
C)  $4.5 \mathrm{ft}^{2}$ 
D)  $324 \mathrm{ft}^{2}$ 
A)  $18 \mathrm{ft}^{2}$ 
B)  $1296 \mathrm{ft}^{2}$ 
C)  $4.5 \mathrm{ft}^{2}$ 
D)  $324 \mathrm{ft}^{2}$

Question 2

The calculator graphs shows the $x$-values of the $x$-intercepts of the graph of the polynomial in the equation. Use the graphs to solve the equation.
-$-x^{2}+2 x+35=0$

Accepted Answer

A)  $\{-35,-2\}$ 
B)  $\{-7,5\}$ 
C)  $\{-5,7\}$ 
D)  $\{5,7\}$ 
A)  $\{-35,-2\}$ 
B)  $\{-7,5\}$ 
C)  $\{-5,7\}$ 
D)  $\{5,7\}$

Question 3

Solve the equation.
-$x^{4}+8 x^{2}-9=0$

Accepted Answer

A)  $\{\mathrm{i},-\mathrm{i}, 3 \mathrm{i},-3 \mathrm{i}\}$ 
B)  $\{3,-3, i,-i\}$ 
C)  $\{1,-1,3 \mathrm{i},-3 \mathrm{i}\}$ 
D)  $\{1,-1,3,-3\}$ 
A)  $\{\mathrm{i},-\mathrm{i}, 3 \mathrm{i},-3 \mathrm{i}\}$ 
B)  $\{3,-3, i,-i\}$ 
C)  $\{1,-1,3 \mathrm{i},-3 \mathrm{i}\}$ 
D)  $\{1,-1,3,-3\}$

Question 4

Use the discriminant of the equation to determine the number of $x$-intercepts.
-$f(x)=-7 x^{2}-14 x+7$

Accepted Answer

A)  One $x$-intercept 
B)  No x-intercepts 
C)  Two $x$-intercepts 
A)  One $x$-intercept 
B)  No x-intercepts 
C)  Two $x$-intercepts

Question 5

Solve the problem. Round your answer to the nearest tenth, when appropriate.
-The position of an object moving in a straight line is given by $s(t)=t^{2}-8 t$, where $s$ is in feet and $t$ is the time in seconds the object has been in motion. How long will it take the object to move $6 \mathrm{ft}$ ?

Accepted Answer

A)  $8.5 \mathrm{sec}$ 
B)  $1.2 \mathrm{sec}$ 
C)  $7.0 \mathrm{sec}$ 
D)  $8.7 \mathrm{sec}$ 
A)  $8.5 \mathrm{sec}$ 
B)  $1.2 \mathrm{sec}$ 
C)  $7.0 \mathrm{sec}$ 
D)  $8.7 \mathrm{sec}$

Question 6

Solve the inequality, and graph the solution set.
-$t^{2}-4 t-5 \leq 0$

Accepted Answer

A)  $(-\infty,-1] \cup[5, \infty)$
  
B)  $[-1,5]$
  
C)  $(-\infty,-1]$
  
D)  $[5, \infty)$
  
A)  $(-\infty,-1] \cup[5, \infty)$
  
B)  $[-1,5]$
  
C)  $(-\infty,-1]$
  
D)  $[5, \infty)$

Question 7

Sketch the graph of the parabola.
-$ y=-\frac{3}{10}(x-6)^{2}+5 $

Accepted Answer

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

Question 8

Choose the equation that matches the graph.
-

Accepted Answer

A)  $f(x)=3 x^{2}-2 x+2$ 
B)  $f(x)=-3 x^{2}-2 x-2$ 
C)  $f(x)=3 x^{2}-2 x-2$ 
D)  $f(x)=3 x^{2}+2 x-2$ 
A)  $f(x)=3 x^{2}-2 x+2$ 
B)  $f(x)=-3 x^{2}-2 x-2$ 
C)  $f(x)=3 x^{2}-2 x-2$ 
D)  $f(x)=3 x^{2}+2 x-2$

Question 9

Choose the equation that matches the graph.
-

Accepted Answer

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

Question 10

Graph the parabola. Identify the vertex, axis, domain and range.
-$f(x)=-x^{2}+2 x+2$

Accepted Answer

A)  Vertex: $(-1,1)$; Axis: $\mathrm{x}=-1$;
Domain: $(\infty, \infty)$; Range: $[1, \infty)$
  
B)  Vertex: (1, -1); Axis: $\mathrm{x}=1$;
Domain: $(\infty, \infty)$; Range: $[1, \infty)$
  
C)  Vertex: (1, -1); Axis: $\mathrm{x}=1$;
Domain: $(\infty, \infty)$; Range: $[1, \infty)$
  
D)  Vertex: $(1,3)$; Axis: $\mathrm{x}=1$;
Domain: $(\infty, \infty)$; Range: $(\infty, 3]$
  
A)  Vertex: $(-1,1)$; Axis: $\mathrm{x}=-1$;
Domain: $(\infty, \infty)$; Range: $[1, \infty)$
  
B)  Vertex: (1, -1); Axis: $\mathrm{x}=1$;
Domain: $(\infty, \infty)$; Range: $[1, \infty)$
  
C)  Vertex: (1, -1); Axis: $\mathrm{x}=1$;
Domain: $(\infty, \infty)$; Range: $[1, \infty)$
  
D)  Vertex: $(1,3)$; Axis: $\mathrm{x}=1$;
Domain: $(\infty, \infty)$; Range: $(\infty, 3]$

Question 11

True or false? The equation $(7 x-4)^{2}=-39$ has two real solutions. If false, give the correct number of real solutions.

Accepted Answer

A)  False; three 
B)  False; zero 
C)  False; one 
D)  True 
A)  False; three 
B)  False; zero 
C)  False; one 
D)  True

Question 12

Use the ordered pairs $(2,14.74),(6,11.46)$, and $(8,12.94)$ to find a quadratic function that models the data. Round the values of $a, b$, and $c$ to two decimal places.

Accepted Answer

A)  $y=2.9 x^{2}-0.26 x+19.50$ 
B)  $y=-2.90 x^{2}+0.26 x+19.50$ 
C)  $y=-2.90 x^{2}+0.26 x+20.5$ 
D)  $y=0.26 x^{2}-2.90 x+19.50$ 
A)  $y=2.9 x^{2}-0.26 x+19.50$ 
B)  $y=-2.90 x^{2}+0.26 x+19.50$ 
C)  $y=-2.90 x^{2}+0.26 x+20.5$ 
D)  $y=0.26 x^{2}-2.90 x+19.50$

Question 13

Solve the problem. Round your answer to the nearest tenth, if necessary.
-Ron takes two hr more time than Paul to mow the lawn. Working together they can mow the lawn in $5 \mathrm{hr}$. How long does it take each of them working alone?

Accepted Answer

A)  Paul: $10 \mathrm{hr}$; Ron: $12 \mathrm{hr}$ 
B)  Paul: $9.1 \mathrm{hr}$; Ron: $11.1 \mathrm{hr}$ 
C)  Paul: 8.3 hr; Ron: 10.3 hr 
D)  Paul: $8 \mathrm{hr}$; Ron: $10 \mathrm{hr}$ 
A)  Paul: $10 \mathrm{hr}$; Ron: $12 \mathrm{hr}$ 
B)  Paul: $9.1 \mathrm{hr}$; Ron: $11.1 \mathrm{hr}$ 
C)  Paul: 8.3 hr; Ron: 10.3 hr 
D)  Paul: $8 \mathrm{hr}$; Ron: $10 \mathrm{hr}$

Question 14

The length and width of a rectangular playlot have a sum of 82 yards. What dimensions would give the maximum area?

Accepted Answer

A)  Length 31 yards and width 51 yards 
B)  Length 40 yards and width 42 yards 
C)  Length 41 yards and width 41 yards 
D)  Length 32 yards and width 50 yards 
A)  Length 31 yards and width 51 yards 
B)  Length 40 yards and width 42 yards 
C)  Length 41 yards and width 41 yards 
D)  Length 32 yards and width 50 yards

Question 15

Find the vertex of the parabola
-$f(x)=-3 x^{2}+6 x-8$

Accepted Answer

A)  $(-1,5)$ 
B)  $(1,-5)$ 
C)  $(-5,1)$ 
D)  $(5,-1)$ 
A)  $(-1,5)$ 
B)  $(1,-5)$ 
C)  $(-5,1)$ 
D)  $(5,-1)$

Question 16

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it.
-$16 m^{2}-10 m-21=0$

Accepted Answer

A)  $(8 m-3)(2 m+7)=0$ 
B)  $(16 m+3)(m+7)=0$ 
C)  $(2 m-3)(8 m+7)=0$ 
D)  Cannot be solved by factoring 
A)  $(8 m-3)(2 m+7)=0$ 
B)  $(16 m+3)(m+7)=0$ 
C)  $(2 m-3)(8 m+7)=0$ 
D)  Cannot be solved by factoring

Question 17

Choose the one alternative that best completes the statement or answers the question.
-Which method of solving the following equation would probably be more convenient? $(5 x-4)^{2}=24$

Accepted Answer

A)  Completing the square 
B)  Square root property 
A)  Completing the square 
B)  Square root property

Question 18

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve.
-$\mathrm{v}^{2}-5 \mathrm{v}-2=0$

Accepted Answer

A)  One rational solution 
B)  Two nonreal complex solutions 
C)  Two irrational solutions 
D)  Two rational solutions 
A)  One rational solution 
B)  Two nonreal complex solutions 
C)  Two irrational solutions 
D)  Two rational solutions

Question 19

Consider the rational inequality $\frac{6}{x^{2}+7}<0$. Without doing any work, give the solution set. (Hint: determine the sign of the numerator and denominator.)

Accepted Answer

A)  $(7,6)$ 
B)  $(-\infty, \infty)$ 
C)  $(7, \infty)$ 
D)  $\varnothing$ 
A)  $(7,6)$ 
B)  $(-\infty, \infty)$ 
C)  $(7, \infty)$ 
D)  $\varnothing$

Question 20

Solve the inequality, and graph the solution set.
-$\frac{(x-3)(x+7)}{x-4} \leq 0$

Accepted Answer

A)  $ (-\infty,-7) \cup(3,4) $
  
B)  $ [-7,3] \cup(4, \infty) $
  
C)  $ [3,4) $
  
D)  $ (-\infty,-7] \cup[3,4) $
  
A)  $ (-\infty,-7) \cup(3,4) $
  
B)  $ [-7,3] \cup(4, \infty) $
  
C)  $ [3,4) $
  
D)  $ (-\infty,-7] \cup[3,4) $

A gardener is fencing off a rectangular area with a fixed perimeter of $72 \mathrm{ft}$ . What is the maximum area?

Solve the equation. - $x^{4}+8 x^{2}-9=0$

Use the discriminant of the equation to determine the number of $x$ -intercepts. - $f(x)=-7 x^{2}-14 x+7$

Solve the inequality, and graph the solution set. - $t^{2}-4 t-5 \leq 0$ $Solve the inequality, and graph the solution set. - t^{2}-4 t-5 \leq 0$

Sketch the graph of the parabola. - $y=-\frac{3}{10}(x-6)^{2}+5$ $Sketch the graph of the parabola. - y=-\frac{3}{10}(x-6)^{2}+5$

Choose the equation that matches the graph. -

Choose the equation that matches the graph. -

Graph the parabola. Identify the vertex, axis, domain and range. - $f(x)=-x^{2}+2 x+2$ $Graph the parabola. Identify the vertex, axis, domain and range. - f(x)=-x^{2}+2 x+2$

True or false? The equation $(7 x-4)^{2}=-39$ has two real solutions. If false, give the correct number of real solutions.

Use the ordered pairs $(2,14.74),(6,11.46)$ , and $(8,12.94)$ to find a quadratic function that models the data. Round the values of $a, b$ , and $c$ to two decimal places.

Solve the problem. Round your answer to the nearest tenth, if necessary. -Ron takes two hr more time than Paul to mow the lawn. Working together they can mow the lawn in $5 \mathrm{hr}$ . How long does it take each of them working alone?

The length and width of a rectangular playlot have a sum of 82 yards. What dimensions would give the maximum area?

Find the vertex of the parabola - $f(x)=-3 x^{2}+6 x-8$

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - $16 m^{2}-10 m-21=0$

Choose the one alternative that best completes the statement or answers the question. -Which method of solving the following equation would probably be more convenient? $(5 x-4)^{2}=24$

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve. - $\mathrm{v}^{2}-5 \mathrm{v}-2=0$

Consider the rational inequality $\frac{6}{x^{2}+7}<0$ . Without doing any work, give the solution set. (Hint: determine the sign of the numerator and denominator.)

Solve the inequality, and graph the solution set. - $\frac{(x-3)(x+7)}{x-4} \leq 0$ $Solve the inequality, and graph the solution set. - \frac{(x-3)(x+7)}{x-4} \leq 0$

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

A gardener is fencing off a rectangular area with a fixed perimeter of 72ft72 \mathrm{ft}72ft . What is the maximum area?

The calculator graphs shows the xxx -values of the xxx -intercepts of the graph of the polynomial in the equation. Use the graphs to solve the equation. - −x2+2x+35=0-x^{2}+2 x+35=0−x2+2x+35=0

Solve the equation. - x4+8x2−9=0x^{4}+8 x^{2}-9=0x4+8x2−9=0

Use the discriminant of the equation to determine the number of xxx -intercepts. - f(x)=−7x2−14x+7f(x)=-7 x^{2}-14 x+7f(x)=−7x2−14x+7

Solve the inequality, and graph the solution set. - t2−4t−5≤0t^{2}-4 t-5 \leq 0t2−4t−5≤0

Sketch the graph of the parabola. - y=−310(x−6)2+5 y=-\frac{3}{10}(x-6)^{2}+5 y=−103​(x−6)2+5

Choose the equation that matches the graph. -

Choose the equation that matches the graph. -

Graph the parabola. Identify the vertex, axis, domain and range. - f(x)=−x2+2x+2f(x)=-x^{2}+2 x+2f(x)=−x2+2x+2

True or false? The equation (7x−4)2=−39(7 x-4)^{2}=-39(7x−4)2=−39 has two real solutions. If false, give the correct number of real solutions.

Use the ordered pairs (2,14.74),(6,11.46)(2,14.74),(6,11.46)(2,14.74),(6,11.46) , and (8,12.94)(8,12.94)(8,12.94) to find a quadratic function that models the data. Round the values of a,ba, ba,b , and ccc to two decimal places.

Solve the problem. Round your answer to the nearest tenth, if necessary. -Ron takes two hr more time than Paul to mow the lawn. Working together they can mow the lawn in 5hr5 \mathrm{hr}5hr . How long does it take each of them working alone?

The length and width of a rectangular playlot have a sum of 82 yards. What dimensions would give the maximum area?

Find the vertex of the parabola - f(x)=−3x2+6x−8f(x)=-3 x^{2}+6 x-8f(x)=−3x2+6x−8

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - 16m2−10m−21=016 m^{2}-10 m-21=016m2−10m−21=0

Choose the one alternative that best completes the statement or answers the question. -Which method of solving the following equation would probably be more convenient? (5x−4)2=24(5 x-4)^{2}=24(5x−4)2=24

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve. - v2−5v−2=0\mathrm{v}^{2}-5 \mathrm{v}-2=0v2−5v−2=0

Consider the rational inequality 6x2+7<0\frac{6}{x^{2}+7}<0x2+76​<0 . Without doing any work, give the solution set. (Hint: determine the sign of the numerator and denominator.)

Solve the inequality, and graph the solution set. - (x−3)(x+7)x−4≤0\frac{(x-3)(x+7)}{x-4} \leq 0x−4(x−3)(x+7)​≤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

A gardener is fencing off a rectangular area with a fixed perimeter of $72 \mathrm{ft}$ . What is the maximum area?

Solve the equation. - $x^{4}+8 x^{2}-9=0$

Use the discriminant of the equation to determine the number of $x$ -intercepts. - $f(x)=-7 x^{2}-14 x+7$

Solve the inequality, and graph the solution set. - $t^{2}-4 t-5 \leq 0$ $Solve the inequality, and graph the solution set. - t^{2}-4 t-5 \leq 0$

Sketch the graph of the parabola. - $y=-\frac{3}{10}(x-6)^{2}+5$ $Sketch the graph of the parabola. - y=-\frac{3}{10}(x-6)^{2}+5$

Graph the parabola. Identify the vertex, axis, domain and range. - $f(x)=-x^{2}+2 x+2$ $Graph the parabola. Identify the vertex, axis, domain and range. - f(x)=-x^{2}+2 x+2$

True or false? The equation $(7 x-4)^{2}=-39$ has two real solutions. If false, give the correct number of real solutions.

Use the ordered pairs $(2,14.74),(6,11.46)$ , and $(8,12.94)$ to find a quadratic function that models the data. Round the values of $a, b$ , and $c$ to two decimal places.

Solve the problem. Round your answer to the nearest tenth, if necessary. -Ron takes two hr more time than Paul to mow the lawn. Working together they can mow the lawn in $5 \mathrm{hr}$ . How long does it take each of them working alone?

Find the vertex of the parabola - $f(x)=-3 x^{2}+6 x-8$

Use the discriminant to determine if the equation can be solved by factoring. If the equation can be solved by factoring, then factor it. - $16 m^{2}-10 m-21=0$

Choose the one alternative that best completes the statement or answers the question. -Which method of solving the following equation would probably be more convenient? $(5 x-4)^{2}=24$

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrational solutions, or two nonreal complex solutions. Do not actually solve. - $\mathrm{v}^{2}-5 \mathrm{v}-2=0$

Consider the rational inequality $\frac{6}{x^{2}+7}<0$ . Without doing any work, give the solution set. (Hint: determine the sign of the numerator and denominator.)

Solve the inequality, and graph the solution set. - $\frac{(x-3)(x+7)}{x-4} \leq 0$ $Solve the inequality, and graph the solution set. - \frac{(x-3)(x+7)}{x-4} \leq 0$