Question 1

Find the axis of symmetry associated with the quadratic equation.
-$y=x^{2}-14 x+49$

Accepted Answer

A)  $x=7$ 
B)  $x=-7$ 
C)  $x=1$ 
D)  $x=-1$ 
A)  $x=7$ 
B)  $x=-7$ 
C)  $x=1$ 
D)  $x=-1$

Question 2

Graph the piecewise function
-$f(x)=\left\{\begin{array}{l}(x+4)^{3}+1 \text { if } x \leq-3 \ \sqrt{x+7}+2 \text { if } x>-3\end{array}\right.$

Accepted Answer

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

Question 3

Without graphing the function, state the shift(s) that are applied to the graph of $f(x)=x^{2}$ to graph the given function. If the graph of $f(x)=x^{2}$ must be rotated about the $x$-axis, state this.
-$f(x)=-(x-2)^{2}+7$

Accepted Answer

A)  right 2 units, up 7 units 
B)  rotate about $x$ - axis, right 2 units, up 7 units 
C)  right 7 units, down 2 units 
D)  rotate about $\mathrm{x}$ - axis, left 2 units, up 7 units 
A)  right 2 units, up 7 units 
B)  rotate about $x$ - axis, right 2 units, up 7 units 
C)  right 7 units, down 2 units 
D)  rotate about $\mathrm{x}$ - axis, left 2 units, up 7 units

Question 4

The Hardy- Weinberg principle that states if $p$ is the frequency of the dominant allele $A$ in a gene pool and $q$ is the frequency of the recessive allele $a$ in the gene pool, then $p+q=1$ and $\mathrm{p}^{2}+2 \mathrm{pq}+\mathrm{q}^{2}=1$.
*Portion of the population that is homozygous dominant (AA): $\mathrm{p}^{2}$
*Portion of the population that is heterozygous dominant (Aa): 2pq
*Portion of the population that is homozygous recessive (aa): $\mathrm{q}^{2}$
Sickle-cell anemia is a recessive genetic condition, meaning that a person only has the disease if both alleles are recessive. If $0.35 \%$ of a population has sickle- cell anemia, what percentage of the population is homozygous dominant and what percentage is heterozygous dominant? Round $\mathrm{q}$ and $\mathrm{p}$ to the nearest thousandth, and round percentages to the nearest tenth of a perœent.

Accepted Answer

A)  homozygous dominant: $86.2 \%$, heterozygous dominant: $12.8 \%$ 
B)  homozygous dominant: $94.1 \%$, heterozygous dominant: $5.9 \%$ 
C)  homozygous dominant: 94.5\%, heterozygous dominant: $5.5 \%$ 
D)  homozygous dominant: 88.5\%, heterozygous dominant: $11.1 \%$ 
A)  homozygous dominant: $86.2 \%$, heterozygous dominant: $12.8 \%$ 
B)  homozygous dominant: $94.1 \%$, heterozygous dominant: $5.9 \%$ 
C)  homozygous dominant: 94.5\%, heterozygous dominant: $5.5 \%$ 
D)  homozygous dominant: 88.5\%, heterozygous dominant: $11.1 \%$

Question 5

Solve by extracting square roots
-$\left(x-\frac{3}{4}\right)^{2}=-\frac{25}{16}$

Accepted Answer

A)  $\left\{\frac{-3 \pm 5 i}{4}\right\}$ 
B)  $\left\{\frac{-3 \pm 5 i}{16}\right\}$ 
C)  $\left\{\frac{3 \pm 5 \mathrm{i}}{16}\right\}$ 
D)  $\left\{\frac{3 \pm 5 \mathrm{i}}{4}\right\}$ 
A)  $\left\{\frac{-3 \pm 5 i}{4}\right\}$ 
B)  $\left\{\frac{-3 \pm 5 i}{16}\right\}$ 
C)  $\left\{\frac{3 \pm 5 \mathrm{i}}{16}\right\}$ 
D)  $\left\{\frac{3 \pm 5 \mathrm{i}}{4}\right\}$

Question 6

Solve the equation.
-$\frac{4}{3 x}-\frac{1}{x+1}=\frac{1}{2 x^{2}+2 x}$

Accepted Answer

A)  $\{-5\}$ 
B)  $\left\{-\frac{5}{2}\right\}$ 
C)  $\left\{-\frac{5}{6}\right\}$ 
D)  $\varnothing$ 
A)  $\{-5\}$ 
B)  $\left\{-\frac{5}{2}\right\}$ 
C)  $\left\{-\frac{5}{6}\right\}$ 
D)  $\varnothing$

Question 7

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

Accepted Answer

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

Question 8

Given $f(x)=x^{2}+13 x+42$, find all values for $x$ for which $f(x)>0$.

Accepted Answer

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

Question 9

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form.
-$x^{2}+3 x$

Accepted Answer

A)  $0 ;(x+3)^{2}$ 
B)  $\frac{9}{4} ;\left(x+\frac{3}{2}\right)^{2}$ 
C)  $\frac{9}{4} ;\left(x-\frac{3}{2}\right)^{2}$ 
D)  0 ; $\left(x+\frac{3}{2}\right)^{2}$ 
A)  $0 ;(x+3)^{2}$ 
B)  $\frac{9}{4} ;\left(x+\frac{3}{2}\right)^{2}$ 
C)  $\frac{9}{4} ;\left(x-\frac{3}{2}\right)^{2}$ 
D)  0 ; $\left(x+\frac{3}{2}\right)^{2}$

Question 10

Find $b$ such that the average rate of change of the function $f(x)$ on the interval is equal to the given value.
-$f(x)=x^{2}+6 x+10,[3, b]$; average rate of change: 19

Accepted Answer

A)  $b=13$ 
B)  $b=10$ 
C)  $b=1$ 
D)  $b=7$ 
A)  $b=13$ 
B)  $b=10$ 
C)  $b=1$ 
D)  $b=7$

Question 11

A rectangular space of 390 square feet is allocated for the living and dining areas in an apartment. Find the width of the square living area given that the width of the dining area is $11 \mathrm{ft}$.

Accepted Answer

A)  $14 \mathrm{ft}$ 
B)  $17 \mathrm{ft}$ 
C)  $26 \mathrm{ft}$ 
D)  $15 \mathrm{ft}$ 
A)  $14 \mathrm{ft}$ 
B)  $17 \mathrm{ft}$ 
C)  $26 \mathrm{ft}$ 
D)  $15 \mathrm{ft}$

Question 12

Solve by factoring.
-$x^{2}+7 x-18=0$

Accepted Answer

A)  $\{9,2\}$ 
B)  $\{2,9\}$ 
C)  $\{-9,2\}$ 
D)  $\{9,-2\}$ 
A)  $\{9,2\}$ 
B)  $\{2,9\}$ 
C)  $\{-9,2\}$ 
D)  $\{9,-2\}$

Question 13

Given $f(x)=x^{2}-18 x+70$, find all values for $x$ for which $f(x) \geq 0$.

Accepted Answer

A)  $[9-\sqrt{11}, 9+\sqrt{11}]$ 
B)  $(-\infty,-\sqrt{11}] \cup[\sqrt{11}, \infty)$ 
C)  $(-\infty, 9-\sqrt{11}] \cup[9+\sqrt{11}, \infty)$ 
D)  $(-\infty, 9-\sqrt{11}) \cup(9+\sqrt{11}, \infty)$ 
A)  $[9-\sqrt{11}, 9+\sqrt{11}]$ 
B)  $(-\infty,-\sqrt{11}] \cup[\sqrt{11}, \infty)$ 
C)  $(-\infty, 9-\sqrt{11}] \cup[9+\sqrt{11}, \infty)$ 
D)  $(-\infty, 9-\sqrt{11}) \cup(9+\sqrt{11}, \infty)$

Question 14

Find the average rate of change for $f(x)$ on the given interval.
-$f(x)=(x+4)^{2}+13,[-9,-2]$

Accepted Answer

A)  -6 
B)  3 
C)  -3 
D)  6 
A)  -6 
B)  3 
C)  -3 
D)  6

Question 15

Graph the function, and state its domain and range
-$ f(x)=\frac{1}{5} x^{3} $

Accepted Answer

A)  Domain: $ (-\infty, \infty) $; Range: $ (-\infty, \infty) $
  
B)  Domain: $ (-\infty, \infty) $; Range: $ (-\infty, \infty) $
  
C)  Domain: $ (-\infty, \infty) $; Range: $ (-\infty, \infty) $
  
D)  Domain: $ (-\infty, \infty) $; Range: $ (-\infty, \infty) $
  
A)  Domain: $ (-\infty, \infty) $; Range: $ (-\infty, \infty) $
  
B)  Domain: $ (-\infty, \infty) $; Range: $ (-\infty, \infty) $
  
C)  Domain: $ (-\infty, \infty) $; Range: $ (-\infty, \infty) $
  
D)  Domain: $ (-\infty, \infty) $; Range: $ (-\infty, \infty) $

Question 16

Solve the polynomial inequality. Express your solution on a number line using interval notation.
-$x(x-6)(x+8)(x+5)>0$

Accepted Answer

A)  $ (-\infty,-8) \cup(-5,6) $
  
B)  $ (-\infty,-8) \cup(-5,0) \cup(6, \infty) $
  
C)  $ (-8,-5) \cup(0,6) $
  
D)  $ (0, \infty) $
  
A)  $ (-\infty,-8) \cup(-5,6) $
  
B)  $ (-\infty,-8) \cup(-5,0) \cup(6, \infty) $
  
C)  $ (-8,-5) \cup(0,6) $
  
D)  $ (0, \infty) $

Question 17

State the domain and range of the given function
-$f(x)=-(x-6)^{2}-9$

Accepted Answer

A)  Domain: $(-\infty, \infty)$
Range: $[-9, \infty)$ 
B)  Domain: [ $6, \infty)$
Range: $(-\infty,-9]$ 
C)  Domain: $(-\infty, \infty)$
Range: $(-\infty, \infty)$ 
D)  Domain: $(-\infty, \infty)$
Range: $(-\infty,-9]$ 
A)  Domain: $(-\infty, \infty)$
Range: $[-9, \infty)$ 
B)  Domain: [ $6, \infty)$
Range: $(-\infty,-9]$ 
C)  Domain: $(-\infty, \infty)$
Range: $(-\infty, \infty)$ 
D)  Domain: $(-\infty, \infty)$
Range: $(-\infty,-9]$

Question 18

Solve by using the quadratic formula
-$x^{2}-\frac{4}{3} x+\frac{7}{6}=0$

Accepted Answer

A)  $\left\{0,-\frac{7}{8} \mathrm{i}\right\}$ 
B)  $\left\{\frac{4}{3} \mathrm{i}, 0\right\}$ 
C)  $\left\{\frac{-4 \pm \sqrt{26} \mathrm{i}}{6}\right\}$ 
D)  $\left\{\frac{4 \pm \sqrt{26} i}{6}\right\}$ 
A)  $\left\{0,-\frac{7}{8} \mathrm{i}\right\}$ 
B)  $\left\{\frac{4}{3} \mathrm{i}, 0\right\}$ 
C)  $\left\{\frac{-4 \pm \sqrt{26} \mathrm{i}}{6}\right\}$ 
D)  $\left\{\frac{4 \pm \sqrt{26} i}{6}\right\}$

Question 19

Find the vertex of the parabola associated with the quadratic equation.
-$y=(x-7)^{2}-8$

Accepted Answer

A)  $(-7,8)$ 
B)  $(8,-7)$ 
C)  $(-8,7)$ 
D)  $(7,-8)$ 
A)  $(-7,8)$ 
B)  $(8,-7)$ 
C)  $(-8,7)$ 
D)  $(7,-8)$

Question 20

Solve the rational inequality. Express your solution on a number line using interval notation.
-$\frac{(x+12)(x-2)}{x-1} \geq 0$

Accepted Answer

A)  $ [-12,1] \cup[2, \infty) $
  
B)  $ (-\infty,-12] \cup(1,2] $
  
C)  $ [-12,1) \cup[2, \infty) $
  
D)  $ (-\infty,-12] \cup[2, \infty) $
  
A)  $ [-12,1] \cup[2, \infty) $
  
B)  $ (-\infty,-12] \cup(1,2] $
  
C)  $ [-12,1) \cup[2, \infty) $
  
D)  $ (-\infty,-12] \cup[2, \infty) $

Find the axis of symmetry associated with the quadratic equation. - $y=x^{2}-14 x+49$

Graph the piecewise function - $f(x)=\left\{\begin{array}{l}(x+4)^{3}+1 \text { if } x \leq-3 \\ \sqrt{x+7}+2 \text { if } x>-3\end{array}\right.$ $Graph the piecewise function - f(x)=\left\{\begin{array}{l}(x+4)^{3}+1 \text { if } x \leq-3 \\ \sqrt{x+7}+2 \text { if } x>-3\end{array}\right.$

Without graphing the function, state the shift(s) that are applied to the graph of $f(x)=x^{2}$ to graph the given function. If the graph of $f(x)=x^{2}$ must be rotated about the $x$ -axis, state this. - $f(x)=-(x-2)^{2}+7$

Solve by extracting square roots - $\left(x-\frac{3}{4}\right)^{2}=-\frac{25}{16}$

Solve the equation. - $\frac{4}{3 x}-\frac{1}{x+1}=\frac{1}{2 x^{2}+2 x}$

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

Given $f(x)=x^{2}+13 x+42$ , find all values for $x$ for which $f(x)>0$ .

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form. - $x^{2}+3 x$

Find $b$ such that the average rate of change of the function $f(x)$ on the interval is equal to the given value. - $f(x)=x^{2}+6 x+10,[3, b]$ ; average rate of change: 19

Solve by factoring. - $x^{2}+7 x-18=0$

Given $f(x)=x^{2}-18 x+70$ , find all values for $x$ for which $f(x) \geq 0$ .

Find the average rate of change for $f(x)$ on the given interval. - $f(x)=(x+4)^{2}+13,[-9,-2]$

Graph the function, and state its domain and range - $f(x)=\frac{1}{5} x^{3}$ $Graph the function, and state its domain and range - f(x)=\frac{1}{5} x^{3}$

Solve the polynomial inequality. Express your solution on a number line using interval notation. - $x(x-6)(x+8)(x+5)>0$

State the domain and range of the given function - $f(x)=-(x-6)^{2}-9$

Solve by using the quadratic formula - $x^{2}-\frac{4}{3} x+\frac{7}{6}=0$

Find the vertex of the parabola associated with the quadratic equation. - $y=(x-7)^{2}-8$

Solve the rational inequality. Express your solution on a number line using interval notation. - $\frac{(x+12)(x-2)}{x-1} \geq 0$ $Solve the rational inequality. Express your solution on a number line using interval notation. - \frac{(x+12)(x-2)}{x-1} \geq 0$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Rational Expressions and Equations

Radical Expressions and Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 8: Quadratic Equations

Find the axis of symmetry associated with the quadratic equation. - y=x2−14x+49y=x^{2}-14 x+49y=x2−14x+49

Graph the piecewise function - f(x)={(x+4)3+1 if x≤−3x+7+2 if x>−3f(x)=\left\{\begin{array}{l}(x+4)^{3}+1 \text { if } x \leq-3 \\ \sqrt{x+7}+2 \text { if } x>-3\end{array}\right.f(x)={(x+4)3+1 if x≤−3x+7​+2 if x>−3​

Without graphing the function, state the shift(s) that are applied to the graph of f(x)=x2f(x)=x^{2}f(x)=x2 to graph the given function. If the graph of f(x)=x2f(x)=x^{2}f(x)=x2 must be rotated about the xxx -axis, state this. - f(x)=−(x−2)2+7f(x)=-(x-2)^{2}+7f(x)=−(x−2)2+7

Solve by extracting square roots - (x−34)2=−2516\left(x-\frac{3}{4}\right)^{2}=-\frac{25}{16}(x−43​)2=−1625​

Solve the equation. - 43x−1x+1=12x2+2x\frac{4}{3 x}-\frac{1}{x+1}=\frac{1}{2 x^{2}+2 x}3x4​−x+11​=2x2+2x1​

Graph the given parabola. - y=x2−2xy=x^{2}-2 xy=x2−2x

Given f(x)=x2+13x+42f(x)=x^{2}+13 x+42f(x)=x2+13x+42 , find all values for xxx for which f(x)>0f(x)>0f(x)>0 .

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form. - x2+3xx^{2}+3 xx2+3x

Find bbb such that the average rate of change of the function f(x)f(x)f(x) on the interval is equal to the given value. - f(x)=x2+6x+10,[3,b]f(x)=x^{2}+6 x+10,[3, b]f(x)=x2+6x+10,[3,b] ; average rate of change: 19

A rectangular space of 390 square feet is allocated for the living and dining areas in an apartment. Find the width of the square living area given that the width of the dining area is 11ft11 \mathrm{ft}11ft .

Solve by factoring. - x2+7x−18=0x^{2}+7 x-18=0x2+7x−18=0

Given f(x)=x2−18x+70f(x)=x^{2}-18 x+70f(x)=x2−18x+70 , find all values for xxx for which f(x)≥0f(x) \geq 0f(x)≥0 .

Find the average rate of change for f(x)f(x)f(x) on the given interval. - f(x)=(x+4)2+13,[−9,−2]f(x)=(x+4)^{2}+13,[-9,-2]f(x)=(x+4)2+13,[−9,−2]

Graph the function, and state its domain and range - f(x)=15x3 f(x)=\frac{1}{5} x^{3} f(x)=51​x3

Solve the polynomial inequality. Express your solution on a number line using interval notation. - x(x−6)(x+8)(x+5)>0x(x-6)(x+8)(x+5)>0x(x−6)(x+8)(x+5)>0

State the domain and range of the given function - f(x)=−(x−6)2−9f(x)=-(x-6)^{2}-9f(x)=−(x−6)2−9

Solve by using the quadratic formula - x2−43x+76=0x^{2}-\frac{4}{3} x+\frac{7}{6}=0x2−34​x+67​=0

Find the vertex of the parabola associated with the quadratic equation. - y=(x−7)2−8y=(x-7)^{2}-8y=(x−7)2−8

Solve the rational inequality. Express your solution on a number line using interval notation. - (x+12)(x−2)x−1≥0\frac{(x+12)(x-2)}{x-1} \geq 0x−1(x+12)(x−2)​≥0