Question 1

Identify the vertex of the given parabola.
-$f(x)=x^{2}+2$

Accepted Answer

A)  $(2,0)$ 
B)  $(0,-2)$ 
C)  $(-2,0)$ 
D)  $(0,2)$ 
A)  $(2,0)$ 
B)  $(0,-2)$ 
C)  $(-2,0)$ 
D)  $(0,2)$

Question 2

Determine whether a linear or quadratic function would be a more appropriate model for the graphed data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the coefficient a of $x^{2}$ should be positive or negative.
-

Accepted Answer

A)  Quadratic; negative 
B)  Quadratic; positive 
C)  Linear; positive 
D)  Linear; negative 
A)  Quadratic; negative 
B)  Quadratic; positive 
C)  Linear; positive 
D)  Linear; negative

Question 3

Sketch the graph of the parabola.
-$\ y=(x-4)^2-2$

Accepted Answer

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

Question 4

Solve the inequality.
-$(3+5 x)^{2} \leq-25$

Accepted Answer

A)  $\left[-\frac{8}{5}, \frac{2}{5}\right]$ 
B)  $\left(-\infty,-\frac{8}{5}\right) \cup\left(\frac{2}{5}, \infty\right)$ 
C)  $(-\infty, \infty)$ 
D)  $\varnothing$ 
A)  $\left[-\frac{8}{5}, \frac{2}{5}\right]$ 
B)  $\left(-\infty,-\frac{8}{5}\right) \cup\left(\frac{2}{5}, \infty\right)$ 
C)  $(-\infty, \infty)$ 
D)  $\varnothing$

Question 5

Solve, and graph the solution set.
-$4 x^{2}+17 x \leq 15$

Accepted Answer

A)  $ (-\infty,-5] \cup\left[\frac{3}{4}, \infty\right] $
  
B)  $ \left[-5, \frac{3}{4}\right] $
  
C)  $ [-5, \infty) $
  
D)  $ \left[-\infty, \frac{3}{4}\right] $
  
A)  $ (-\infty,-5] \cup\left[\frac{3}{4}, \infty\right] $
  
B)  $ \left[-5, \frac{3}{4}\right] $
  
C)  $ [-5, \infty) $
  
D)  $ \left[-\infty, \frac{3}{4}\right] $

Question 6

Solve the equation.
-$(7 p-6)^{2}=4(7 p-6)-3$

Accepted Answer

A)  $\{1,3\}$ 
B)  $\left\{-\frac{5}{7},-\frac{3}{7}\right\}$ 
C)  $\left\{-1,-\frac{9}{7}\right\}$ 
D)  $\left\{1, \frac{9}{7}\right\}$ 
A)  $\{1,3\}$ 
B)  $\left\{-\frac{5}{7},-\frac{3}{7}\right\}$ 
C)  $\left\{-1,-\frac{9}{7}\right\}$ 
D)  $\left\{1, \frac{9}{7}\right\}$

Question 7

Sketch the graph of the parabola.
-$\ y = -\frac {{1}}{{6}} x^2 +3 $

Accepted Answer

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

Question 8

Describe how the graph of $y=5 x^{2}$ differs from the graph of $y=x^{2}$.

Accepted Answer

The openin

Question 9

Find the value of $k$ so that the equation will have exactly one rational solution.
-$25 x^{2}-10 x+k=0$

Accepted Answer

A)  -1 
B)  None 
C)  1 
D)  0 
A)  -1 
B)  None 
C)  1 
D)  0

Question 10

Find the vertex of the parabola
-$f(x)=4 x^{2}+16 x+11$

Accepted Answer

A)  $(-5,-2)$ 
B)  $(2,5)$ 
C)  $(5,2)$ 
D)  $(-2,-5)$ 
A)  $(-5,-2)$ 
B)  $(2,5)$ 
C)  $(5,2)$ 
D)  $(-2,-5)$

Question 11

Find the mistake, then find the correct answer.
Solve for $\mathrm{x}:(\mathrm{x}-5)^{2}=-13$
line $1 \quad x-5=\sqrt{13}$
line $2 \quad x=5+\sqrt{13}$ or $x=5-\sqrt{13}$
line 3 The solution set is $\{5+\sqrt{13}, 5-\sqrt{13}\}$.

Accepted Answer

A negative sign was dropped in

Question 12

Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate.
-A rectangular garden has an area of $12 \mathrm{ft}$ by $5 \mathrm{ft}$. A gravel path of equal width is to be built around the garden. How wide can the path be if there is enough gravel for $138 \mathrm{ft}^{2}$ ?

Accepted Answer

A)  $4 \mathrm{ft}$ 
B)  $10 \mathrm{ft}$ 
C)  $5 \mathrm{ft}$ 
D)  $3 \mathrm{ft}$ 
A)  $4 \mathrm{ft}$ 
B)  $10 \mathrm{ft}$ 
C)  $5 \mathrm{ft}$ 
D)  $3 \mathrm{ft}$

Question 13

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.
-$2 x^{2}+5 x-3=0$

Accepted Answer

A)  $\{-2,3\}$ 
B)  $\{-3,-0.5\}$ 
C)  $\{-0.5,3\}$ 
D)  $\{-3,0.5\}$ 
A)  $\{-2,3\}$ 
B)  $\{-3,-0.5\}$ 
C)  $\{-0.5,3\}$ 
D)  $\{-3,0.5\}$

Question 14

A boy is standing on a flat field and tosses his ball toward a second boy standing at the other end of the field. The path of the ball is a parabola, and the equation of the path is $f(x)=-4 x^{2}+8 x$. Based on this information, answer the question.
-What is the highest the ball will be above the flat field and for what value of $x$ ?

Accepted Answer

A)  Highest height $=4$ when $x=2$ 
B)  Highest height $=4$ when $x=1$ 
C)  Cannot determine without additional information 
D)  None of the above 
A)  Highest height $=4$ when $x=2$ 
B)  Highest height $=4$ when $x=1$ 
C)  Cannot determine without additional information 
D)  None of the above

Question 15

Choose the equation that matches the graph.
-

Accepted Answer

A)  $f(x)=-x^{2}+2 x-8$ 
B)  $f(x)=x^{2}+2 x-8$ 
C)  $f(x)=-x^{2}-2 x-8$ 
D)  $f(x)=x^{2}-2 x+8$ 
A)  $f(x)=-x^{2}+2 x-8$ 
B)  $f(x)=x^{2}+2 x-8$ 
C)  $f(x)=-x^{2}-2 x-8$ 
D)  $f(x)=x^{2}-2 x+8$

Question 16

Graph the parabola. Identify the vertex, axis, domain and range.
-$f(x)=-\frac{5}{6} x^{2}+6$

Accepted Answer

A)  Vertex: (0, - 6); Axis: $x=0$;
Domain: $(\infty, \infty)$; Range: $[-6, \infty)$
  
B)  Vertex: $\left(0,-\frac{5}{6}\right)$; Axis: $x=0$;
Domain: $(\infty, \infty)$; Range: $\left[-\frac{5}{6}, \infty\right)$
  
C)  Vertex: $(0,6)$; Axis: $x=0$;
Domain: $(\infty, \infty)$; Range: $[6, \infty)$
  
D)  Vertex: $(0,6)$; Axis: $x=0$;
Domain: $(\infty, \infty)$; Range: $[6, \infty)$
  
A)  Vertex: (0, - 6); Axis: $x=0$;
Domain: $(\infty, \infty)$; Range: $[-6, \infty)$
  
B)  Vertex: $\left(0,-\frac{5}{6}\right)$; Axis: $x=0$;
Domain: $(\infty, \infty)$; Range: $\left[-\frac{5}{6}, \infty\right)$
  
C)  Vertex: $(0,6)$; Axis: $x=0$;
Domain: $(\infty, \infty)$; Range: $[6, \infty)$
  
D)  Vertex: $(0,6)$; Axis: $x=0$;
Domain: $(\infty, \infty)$; Range: $[6, \infty)$

Question 17

Solve the equation.
-$x-17 \sqrt{x}+66=0$

Accepted Answer

A)  $\{6,11\}$ 
B)  $\{36\}$ 
C)  $\{-6,-11\}$ 
D)  $\{36,121\}$ 
A)  $\{6,11\}$ 
B)  $\{36\}$ 
C)  $\{-6,-11\}$ 
D)  $\{36,121\}$

Question 18

Give a one-sentence description or explanation of the square root property.

Accepted Answer

The square root property states that if

Question 19

The number of mosquitoes $M(x)$, in millions, in a certain area depends on the June rainfall $x$, in inches, according to the formula $M(x)=9 x-x^{2}$. What rainfall produces the maximum number of mosquitoes?

Accepted Answer

A)  0 in. 
B)  $81 \mathrm{in.}$ 
C)  4.5 in. 
D)  9 in. 
A)  0 in. 
B)  $81 \mathrm{in.}$ 
C)  4.5 in. 
D)  9 in.

Question 20

Solve the problem. Round your answer to the nearest tenth, if necessary.
-Sue rowed her boat across and back Lake Bend in $3 \mathrm{hr}$. If her rate rowing back was $2 \mathrm{mph}$ less than the rate rowing across, and if the distance each way was $7 \mathrm{mi}$, find her rate rowing across.

Accepted Answer

A)  $5.5 \mathrm{mph}$ 
B)  $1.5 \mathrm{mph}$ 
C)  $5.9 \mathrm{mph}$ 
D)  $3.7 \mathrm{mph}$ 
A)  $5.5 \mathrm{mph}$ 
B)  $1.5 \mathrm{mph}$ 
C)  $5.9 \mathrm{mph}$ 
D)  $3.7 \mathrm{mph}$

Identify the vertex of the given parabola. - $f(x)=x^{2}+2$

Sketch the graph of the parabola. - $\ y=(x-4)^2-2$ $Sketch the graph of the parabola. - \ y=(x-4)^2-2$

Solve the inequality. - $(3+5 x)^{2} \leq-25$

Solve, and graph the solution set. - $4 x^{2}+17 x \leq 15$ $Solve, and graph the solution set. - 4 x^{2}+17 x \leq 15$

Solve the equation. - $(7 p-6)^{2}=4(7 p-6)-3$

Sketch the graph of the parabola. - $\ y = -\frac {{1}}{{6}} x^2 +3$ $Sketch the graph of the parabola. - \ y = -\frac {{1}}{{6}} x^2 +3$

Describe how the graph of $y=5 x^{2}$ differs from the graph of $y=x^{2}$ .

Find the value of $k$ so that the equation will have exactly one rational solution. - $25 x^{2}-10 x+k=0$

Find the vertex of the parabola - $f(x)=4 x^{2}+16 x+11$

Find the mistake, then find the correct answer. Solve for $\mathrm{x}:(\mathrm{x}-5)^{2}=-13$ line $1 \quad x-5=\sqrt{13}$ line $2 \quad x=5+\sqrt{13}$ or $x=5-\sqrt{13}$ line 3 The solution set is $\{5+\sqrt{13}, 5-\sqrt{13}\}$ .

Choose the equation that matches the graph. -

Graph the parabola. Identify the vertex, axis, domain and range. - $f(x)=-\frac{5}{6} x^{2}+6$ $Graph the parabola. Identify the vertex, axis, domain and range. - f(x)=-\frac{5}{6} x^{2}+6$

Solve the equation. - $x-17 \sqrt{x}+66=0$

Give a one-sentence description or explanation of the square root property.

The number of mosquitoes $M(x)$ , in millions, in a certain area depends on the June rainfall $x$ , in inches, according to the formula $M(x)=9 x-x^{2}$ . What rainfall produces the maximum number of mosquitoes?

Solve the problem. Round your answer to the nearest tenth, if necessary. -Sue rowed her boat across and back Lake Bend in $3 \mathrm{hr}$ . If her rate rowing back was $2 \mathrm{mph}$ less than the rate rowing across, and if the distance each way was $7 \mathrm{mi}$ , find her rate rowing across.

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

Identify the vertex of the given parabola. - f(x)=x2+2f(x)=x^{2}+2f(x)=x2+2

Determine whether a linear or quadratic function would be a more appropriate model for the graphed data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the coefficient a of x2x^{2}x2 should be positive or negative. -

Sketch the graph of the parabola. - y=(x−4)2−2\ y=(x-4)^2-2 y=(x−4)2−2

Solve the inequality. - (3+5x)2≤−25(3+5 x)^{2} \leq-25(3+5x)2≤−25

Solve, and graph the solution set. - 4x2+17x≤154 x^{2}+17 x \leq 154x2+17x≤15

Solve the equation. - (7p−6)2=4(7p−6)−3(7 p-6)^{2}=4(7 p-6)-3(7p−6)2=4(7p−6)−3

Sketch the graph of the parabola. - y=−16x2+3\ y = -\frac {{1}}{{6}} x^2 +3 y=−61​x2+3

Describe how the graph of y=5x2y=5 x^{2}y=5x2 differs from the graph of y=x2y=x^{2}y=x2 .

Find the value of kkk so that the equation will have exactly one rational solution. - 25x2−10x+k=025 x^{2}-10 x+k=025x2−10x+k=0

Find the vertex of the parabola - f(x)=4x2+16x+11f(x)=4 x^{2}+16 x+11f(x)=4x2+16x+11

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. - 2x2+5x−3=02 x^{2}+5 x-3=02x2+5x−3=0

Choose the equation that matches the graph. -

Graph the parabola. Identify the vertex, axis, domain and range. - f(x)=−56x2+6f(x)=-\frac{5}{6} x^{2}+6f(x)=−65​x2+6

Solve the equation. - x−17x+66=0x-17 \sqrt{x}+66=0x−17x​+66=0

Give a one-sentence description or explanation of the square root property.

The number of mosquitoes M(x)M(x)M(x) , in millions, in a certain area depends on the June rainfall xxx , in inches, according to the formula M(x)=9x−x2M(x)=9 x-x^{2}M(x)=9x−x2 . What rainfall produces the maximum number of mosquitoes?

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

Identify the vertex of the given parabola. - $f(x)=x^{2}+2$

Sketch the graph of the parabola. - $\ y=(x-4)^2-2$ $Sketch the graph of the parabola. - \ y=(x-4)^2-2$

Solve the inequality. - $(3+5 x)^{2} \leq-25$

Solve, and graph the solution set. - $4 x^{2}+17 x \leq 15$ $Solve, and graph the solution set. - 4 x^{2}+17 x \leq 15$

Solve the equation. - $(7 p-6)^{2}=4(7 p-6)-3$

Sketch the graph of the parabola. - $\ y = -\frac {{1}}{{6}} x^2 +3$ $Sketch the graph of the parabola. - \ y = -\frac {{1}}{{6}} x^2 +3$

Describe how the graph of $y=5 x^{2}$ differs from the graph of $y=x^{2}$ .

Find the value of $k$ so that the equation will have exactly one rational solution. - $25 x^{2}-10 x+k=0$

Find the vertex of the parabola - $f(x)=4 x^{2}+16 x+11$

Graph the parabola. Identify the vertex, axis, domain and range. - $f(x)=-\frac{5}{6} x^{2}+6$ $Graph the parabola. Identify the vertex, axis, domain and range. - f(x)=-\frac{5}{6} x^{2}+6$

Solve the equation. - $x-17 \sqrt{x}+66=0$

The number of mosquitoes $M(x)$ , in millions, in a certain area depends on the June rainfall $x$ , in inches, according to the formula $M(x)=9 x-x^{2}$ . What rainfall produces the maximum number of mosquitoes?