Question 1

Solve by extracting square roots
-$2(x-7)^{2}+12=52$

Accepted Answer

A)  $\{7 \pm 2 \sqrt{5}\}$ 
B)  $\{7 \pm 2 \sqrt{5} i\}$ 
C)  $\{-7 \pm 2 \sqrt{5}\}$ 
D)  $\{-7 \pm 2 \sqrt{5} i\}$ 
A)  $\{7 \pm 2 \sqrt{5}\}$ 
B)  $\{7 \pm 2 \sqrt{5} i\}$ 
C)  $\{-7 \pm 2 \sqrt{5}\}$ 
D)  $\{-7 \pm 2 \sqrt{5} i\}$ A

Question 2

Find the $x$ - and $y$-intercepts of the parabola associated with the quadratic equation. If the parabola does not have any $x$-intercepts, state "no $x$-intercepts."
-$y=(x+3)^{2}-49$

Accepted Answer

A)  $(10,0),(-4,0),(0,-40)$ 
B)  No $x$-intercepts, $(0,-40)$ 
C)  $(10,0),(4,0),(0,40)$ 
D)  $(-10,0),(4,0),(0,-40)$ 
A)  $(10,0),(-4,0),(0,-40)$ 
B)  No $x$-intercepts, $(0,-40)$ 
C)  $(10,0),(4,0),(0,40)$ 
D)  $(-10,0),(4,0),(0,-40)$ D

Question 3

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).
-$6 x^{2}-3 x-9=0$

Accepted Answer

A)  $\left\{\frac{2}{3}, 1\right\}$ 
B)  $\left\{\frac{2}{3}, 0\right\}$ 
C)  $\left\{\frac{2}{3},-1\right\}$ 
D)  $\left\{\frac{3}{2},-1\right\}$ 
A)  $\left\{\frac{2}{3}, 1\right\}$ 
B)  $\left\{\frac{2}{3}, 0\right\}$ 
C)  $\left\{\frac{2}{3},-1\right\}$ 
D)  $\left\{\frac{3}{2},-1\right\}$ D

Question 4

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.
-$x^{2}+8 x$

Accepted Answer

A)  $0 ;(x+4)^{2}$ 
B)  $16 ;(x+4)^{2}$ 
C)  $64 ;(x+8)^{2}$ 
D)  $16 ;(x-4)^{2}$ 
A)  $0 ;(x+4)^{2}$ 
B)  $16 ;(x+4)^{2}$ 
C)  $64 ;(x+8)^{2}$ 
D)  $16 ;(x-4)^{2}$

Question 5

Find the vertex
-$f(x)=-(x+3)^{2}-7$

Accepted Answer

A)  $(3,7)$ 
B)  $(-3,7)$ 
C)  $(-3,-7)$ 
D)  $(3,-7)$ 
A)  $(3,7)$ 
B)  $(-3,7)$ 
C)  $(-3,-7)$ 
D)  $(3,-7)$

Question 6

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).
-$(4 \mathrm{x}+1)^{2}=17$

Accepted Answer

A)  $\left\{\frac{ \pm \sqrt{16}}{4}\right\}$ 
B)  $\left\{\frac{ \pm \sqrt{17}+1}{4}\right\}$ 
C)  $\left\{\frac{-1 \pm \sqrt{17}}{4}\right\}$ 
D)  $\{-1 \pm \sqrt{17}\}$ 
A)  $\left\{\frac{ \pm \sqrt{16}}{4}\right\}$ 
B)  $\left\{\frac{ \pm \sqrt{17}+1}{4}\right\}$ 
C)  $\left\{\frac{-1 \pm \sqrt{17}}{4}\right\}$ 
D)  $\{-1 \pm \sqrt{17}\}$

Question 7

What is the maximum product of two positive numbers whose sum is 16 ?

Accepted Answer

A)  64 
B)  128 
C)  8 
D)  4 
A)  64 
B)  128 
C)  8 
D)  4

Question 8

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.
-$x^{2}-16 x$

Accepted Answer

A)  $64 ;(x+8)^{2}$ 
B)  $64 ;(x-16)^{2}$ 
C)  0 ; $(x-8)^{2}$ 
D)  $64 ;(x-8)^{2}$ 
A)  $64 ;(x+8)^{2}$ 
B)  $64 ;(x-16)^{2}$ 
C)  0 ; $(x-8)^{2}$ 
D)  $64 ;(x-8)^{2}$

Question 9

Given $f(x)=\frac{x^{2}+15 x+50}{x^{2}-6 x-72}$, find all values for $x$ for which $f(x) \geq 0$.

Accepted Answer

A)  $[-10,-6] \cup[-5,12]$ 
B)  $(-\infty,-10] \cup[-6,-5] \cup[12, \infty)$ 
C)  $(-\infty,-10] \cup(-6,-5] \cup(12, \infty)$ 
D)  $[-10,-6) \cup[-5,12)$ 
A)  $[-10,-6] \cup[-5,12]$ 
B)  $(-\infty,-10] \cup[-6,-5] \cup[12, \infty)$ 
C)  $(-\infty,-10] \cup(-6,-5] \cup(12, \infty)$ 
D)  $[-10,-6) \cup[-5,12)$

Question 10

Solve by using the quadratic formula
-$6 x^{2}-3 x-9=0$

Accepted Answer

A)  $\left\{\frac{2}{3}, 1\right\}$ 
B)  $\left\{\frac{2}{3},-1\right\}$ 
C)  $\left\{\frac{2}{3}, 0\right\}$ 
D)  $\left\{\frac{3}{2},-1\right\}$ 
A)  $\left\{\frac{2}{3}, 1\right\}$ 
B)  $\left\{\frac{2}{3},-1\right\}$ 
C)  $\left\{\frac{2}{3}, 0\right\}$ 
D)  $\left\{\frac{3}{2},-1\right\}$

Question 11

Determine a quadratic function that results when applying the given shifts to the graph off(x)=x2.
-$f(x)=-(x+8)^{2}+5$

Accepted Answer

A)  Domain: $(-\infty, \infty)$ Range: $[8, \infty)$ 
B)  Domain: $[8, \infty)$ Range: $(-\infty,-5$ ] 
C)  Domain: $(-\infty, \infty)$ Range: $(-\infty, 5]$ 
D)  Domain: $(-\infty, \infty)$ Range: $[5, \infty)$ 
A)  Domain: $(-\infty, \infty)$ Range: $[8, \infty)$ 
B)  Domain: $[8, \infty)$ Range: $(-\infty,-5$ ] 
C)  Domain: $(-\infty, \infty)$ Range: $(-\infty, 5]$ 
D)  Domain: $(-\infty, \infty)$ Range: $[5, \infty)$

Question 12

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).
-$\frac{3}{4} x^{2}+\frac{1}{2} x+\frac{1}{12}=0$

Accepted Answer

A)  $\left\{\frac{-1+\sqrt{2}}{3}, \frac{-1-\sqrt{2}}{3}\right\}$ 
B)  $\left\{\frac{1}{3},-\frac{1}{3}\right\}$ 
C)  $\left\{\frac{1}{3}\right\}$ 
D)  $\left\{-\frac{1}{3}\right\}$ 
A)  $\left\{\frac{-1+\sqrt{2}}{3}, \frac{-1-\sqrt{2}}{3}\right\}$ 
B)  $\left\{\frac{1}{3},-\frac{1}{3}\right\}$ 
C)  $\left\{\frac{1}{3}\right\}$ 
D)  $\left\{-\frac{1}{3}\right\}$

Question 13

Solve the quadratic inequality. Express your solution on a number line using interval notation.
-$x(x+5) \geq 0$

Accepted Answer

A)  $ (-\infty,-5] $
  
B)  $ [-5,0] $
  
C)  $ [0, \infty) $
  
D)  $ (-\infty,-5] \cup[0, \infty) $
  
A)  $ (-\infty,-5] $
  
B)  $ [-5,0] $
  
C)  $ [0, \infty) $
  
D)  $ (-\infty,-5] \cup[0, \infty) $

Question 14

Graph the given parabola.
-y = -4x2 + 24x - 37

Accepted Answer

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

Question 15

Determine the function $f(x)$ that has been graphed. The function will be of the form $f(x) a \sqrt{x-h}+k$ or $f(x)=a(x-h)^{3}+k$. Assume $a=1$ or $a=-1$.
-

Accepted Answer

A)  $f(x)=-\sqrt{x-1}-5$ 
B)  $f(x)=-\sqrt{x+1}-5$ 
C)  $f(x)=-\sqrt{x+1}+5$ 
D)  $f(x)=-\sqrt{x-1}+5$ 
A)  $f(x)=-\sqrt{x-1}-5$ 
B)  $f(x)=-\sqrt{x+1}-5$ 
C)  $f(x)=-\sqrt{x+1}+5$ 
D)  $f(x)=-\sqrt{x-1}+5$

Question 16

Given $f(x)=x^{2}+2 x-11$ find all values for $x$ for which $f(x) \leq-3$.

Accepted Answer

A)  $\varnothing$ 
B)  $(-4,2)$ 
C)  $(-\infty,-4] \cup[2, \infty)$ 
D)  $[-4,2]$ 
A)  $\varnothing$ 
B)  $(-4,2)$ 
C)  $(-\infty,-4] \cup[2, \infty)$ 
D)  $[-4,2]$

Question 17

Find the $x$ - and $y$-intercepts. If no $x$-intercepts exist, state so.
-$f(x)=4 x^{2}+10 x+3$

Accepted Answer

A)  $\left(\frac{-5 \pm \sqrt{13}}{8}, 0\right),(0,-3)$ 
B)  $\left(\frac{-5 \pm \sqrt{37}}{4}, 0\right),(0,-3)$ 
C)  $\left(\frac{-10 \pm \sqrt{13}}{4}, 0\right),(0,3)$ 
D)  $\left(\frac{-5 \pm \sqrt{13}}{4}, 0\right),(0,3)$ 
A)  $\left(\frac{-5 \pm \sqrt{13}}{8}, 0\right),(0,-3)$ 
B)  $\left(\frac{-5 \pm \sqrt{37}}{4}, 0\right),(0,-3)$ 
C)  $\left(\frac{-10 \pm \sqrt{13}}{4}, 0\right),(0,3)$ 
D)  $\left(\frac{-5 \pm \sqrt{13}}{4}, 0\right),(0,3)$

Question 18

The length of a table is 19 inches more than its width. If the area of the table is 780 square inches, what is its length?

Accepted Answer

A)  $40 \mathrm{in}$. 
B)  $39 \mathrm{in}$. 
C)  1 in. 
D)  $20 \mathrm{in}$. 
A)  $40 \mathrm{in}$. 
B)  $39 \mathrm{in}$. 
C)  1 in. 
D)  $20 \mathrm{in}$.

Question 19

Solve by extracting square roots
-$(x+6)^{2}=5$

Accepted Answer

A)  $\{6 \pm \sqrt{5}\}$ 
B)  $\{6 \pm \sqrt{5} i\}$ 
C)  $\{-6 \pm \sqrt{5} i\}$ 
D)  $\{-6 \pm \sqrt{5}\}$ 
A)  $\{6 \pm \sqrt{5}\}$ 
B)  $\{6 \pm \sqrt{5} i\}$ 
C)  $\{-6 \pm \sqrt{5} i\}$ 
D)  $\{-6 \pm \sqrt{5}\}$

Question 20

Solve by using the quadratic formula
-$x^{2}-24=0$

Accepted Answer

A)  $\{ \pm 12\}$ 
B)  $\{\pm6 \sqrt{2}\}$ 
C)  $\{ \pm 2 \sqrt{6}\}$ 
D)  $\{576\}$ 
A)  $\{ \pm 12\}$ 
B)  $\{\pm6 \sqrt{2}\}$ 
C)  $\{ \pm 2 \sqrt{6}\}$ 
D)  $\{576\}$

Solve by extracting square roots - $2(x-7)^{2}+12=52$

Find the $x$ - and $y$ -intercepts of the parabola associated with the quadratic equation. If the parabola does not have any $x$ -intercepts, state "no $x$ -intercepts." - $y=(x+3)^{2}-49$

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - $6 x^{2}-3 x-9=0$

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. - $x^{2}+8 x$

Find the vertex - $f(x)=-(x+3)^{2}-7$

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - $(4 \mathrm{x}+1)^{2}=17$

What is the maximum product of two positive numbers whose sum is 16 ?

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. - $x^{2}-16 x$

Given $f(x)=\frac{x^{2}+15 x+50}{x^{2}-6 x-72}$ , find all values for $x$ for which $f(x) \geq 0$ .

Solve by using the quadratic formula - $6 x^{2}-3 x-9=0$

Determine a quadratic function that results when applying the given shifts to the graph off(x)=x2. - $f(x)=-(x+8)^{2}+5$

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - $\frac{3}{4} x^{2}+\frac{1}{2} x+\frac{1}{12}=0$

Solve the quadratic inequality. Express your solution on a number line using interval notation. - $x(x+5) \geq 0$ $Solve the quadratic inequality. Express your solution on a number line using interval notation. - x(x+5) \geq 0$

Graph the given parabola. -y = -4x² + 24x - 37

Given $f(x)=x^{2}+2 x-11$ find all values for $x$ for which $f(x) \leq-3$ .

Find the $x$ - and $y$ -intercepts. If no $x$ -intercepts exist, state so. - $f(x)=4 x^{2}+10 x+3$

The length of a table is 19 inches more than its width. If the area of the table is 780 square inches, what is its length?

Solve by extracting square roots - $(x+6)^{2}=5$

Solve by using the quadratic formula - $x^{2}-24=0$

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

Solve by extracting square roots - 2(x−7)2+12=522(x-7)^{2}+12=522(x−7)2+12=52

Find the xxx - and yyy -intercepts of the parabola associated with the quadratic equation. If the parabola does not have any xxx -intercepts, state "no xxx -intercepts." - y=(x+3)2−49y=(x+3)^{2}-49y=(x+3)2−49

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - 6x2−3x−9=06 x^{2}-3 x-9=06x2−3x−9=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+8xx^{2}+8 xx2+8x

Find the vertex - f(x)=−(x+3)2−7f(x)=-(x+3)^{2}-7f(x)=−(x+3)2−7

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - (4x+1)2=17(4 \mathrm{x}+1)^{2}=17(4x+1)2=17

What is the maximum product of two positive numbers whose sum is 16 ?

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. - x2−16xx^{2}-16 xx2−16x

Given f(x)=x2+15x+50x2−6x−72f(x)=\frac{x^{2}+15 x+50}{x^{2}-6 x-72}f(x)=x2−6x−72x2+15x+50​ , find all values for xxx for which f(x)≥0f(x) \geq 0f(x)≥0 .

Solve by using the quadratic formula - 6x2−3x−9=06 x^{2}-3 x-9=06x2−3x−9=0

Determine a quadratic function that results when applying the given shifts to the graph off(x)=x2. - f(x)=−(x+8)2+5f(x)=-(x+8)^{2}+5f(x)=−(x+8)2+5

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - 34x2+12x+112=0\frac{3}{4} x^{2}+\frac{1}{2} x+\frac{1}{12}=043​x2+21​x+121​=0

Solve the quadratic inequality. Express your solution on a number line using interval notation. - x(x+5)≥0x(x+5) \geq 0x(x+5)≥0

Graph the given parabola. -y = -4x2 + 24x - 37

Determine the function f(x)f(x)f(x) that has been graphed. The function will be of the form f(x)ax−h+kf(x) a \sqrt{x-h}+kf(x)ax−h​+k or f(x)=a(x−h)3+kf(x)=a(x-h)^{3}+kf(x)=a(x−h)3+k . Assume a=1a=1a=1 or a=−1a=-1a=−1 . -

Given f(x)=x2+2x−11f(x)=x^{2}+2 x-11f(x)=x2+2x−11 find all values for xxx for which f(x)≤−3f(x) \leq-3f(x)≤−3 .

Find the xxx - and yyy -intercepts. If no xxx -intercepts exist, state so. - f(x)=4x2+10x+3f(x)=4 x^{2}+10 x+3f(x)=4x2+10x+3

The length of a table is 19 inches more than its width. If the area of the table is 780 square inches, what is its length?

Solve by extracting square roots - (x+6)2=5(x+6)^{2}=5(x+6)2=5

Solve by using the quadratic formula - x2−24=0x^{2}-24=0x2−24=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

Solve by extracting square roots - $2(x-7)^{2}+12=52$

Find the $x$ - and $y$ -intercepts of the parabola associated with the quadratic equation. If the parabola does not have any $x$ -intercepts, state "no $x$ -intercepts." - $y=(x+3)^{2}-49$

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - $6 x^{2}-3 x-9=0$

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. - $x^{2}+8 x$

Find the vertex - $f(x)=-(x+3)^{2}-7$

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - $(4 \mathrm{x}+1)^{2}=17$

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. - $x^{2}-16 x$

Given $f(x)=\frac{x^{2}+15 x+50}{x^{2}-6 x-72}$ , find all values for $x$ for which $f(x) \geq 0$ .

Solve by using the quadratic formula - $6 x^{2}-3 x-9=0$

Determine a quadratic function that results when applying the given shifts to the graph off(x)=x2. - $f(x)=-(x+8)^{2}+5$

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - $\frac{3}{4} x^{2}+\frac{1}{2} x+\frac{1}{12}=0$

Solve the quadratic inequality. Express your solution on a number line using interval notation. - $x(x+5) \geq 0$ $Solve the quadratic inequality. Express your solution on a number line using interval notation. - x(x+5) \geq 0$

Graph the given parabola. -y = -4x² + 24x - 37

Given $f(x)=x^{2}+2 x-11$ find all values for $x$ for which $f(x) \leq-3$ .

Find the $x$ - and $y$ -intercepts. If no $x$ -intercepts exist, state so. - $f(x)=4 x^{2}+10 x+3$

Solve by extracting square roots - $(x+6)^{2}=5$

Solve by using the quadratic formula - $x^{2}-24=0$