Question 1

Solve by making a u-substitution
-$x^{4}-33 x^{2}+32=0$

Accepted Answer

A)  $\{ \pm 1, \pm 4 \sqrt{2}\}$ 
B)  $\{ \pm 2, \pm 4\}$ 
C)  $\{ \pm 1, \pm 4 \sqrt{3}\}$ 
D)  $\{ \pm 1, \pm \sqrt{2}\}$ 
A)  $\{ \pm 1, \pm 4 \sqrt{2}\}$ 
B)  $\{ \pm 2, \pm 4\}$ 
C)  $\{ \pm 1, \pm 4 \sqrt{3}\}$ 
D)  $\{ \pm 1, \pm \sqrt{2}\}$

Question 2

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value.
-$f(x)=(x-2)^{2}+2$

Accepted Answer

A)  Minimum, 2 
B)  Maximum, - 2 
C)  Minimum, - 2 
D)  Maximum, 2 
A)  Minimum, 2 
B)  Maximum, - 2 
C)  Minimum, - 2 
D)  Maximum, 2

Question 3

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula).
-$(6 \mathrm{x}+9)^{2}=16$

Accepted Answer

A)  $\left\{-\frac{5}{6}, 0\right\}$ 
B)  $\left\{\frac{5}{6}, \frac{13}{6}\right\}$ 
C)  $\left\{-\frac{5}{6},-\frac{13}{6}\right\}$ 
D)  $\left\{\frac{7}{6}\right\}$ 
A)  $\left\{-\frac{5}{6}, 0\right\}$ 
B)  $\left\{\frac{5}{6}, \frac{13}{6}\right\}$ 
C)  $\left\{-\frac{5}{6},-\frac{13}{6}\right\}$ 
D)  $\left\{\frac{7}{6}\right\}$

Question 4

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)  $f(x)=x^{3}-1$ 
B)  $f(x)=x^{3}+1$ 
C)  $f(x)=(x+1)^{3}$ 
D)  $f(x)=(x-1)^{3}$ 
A)  $f(x)=x^{3}-1$ 
B)  $f(x)=x^{3}+1$ 
C)  $f(x)=(x+1)^{3}$ 
D)  $f(x)=(x-1)^{3}$

Question 5

Solve the equation.
-$\sqrt{2 \mathrm{x}+5}=3+\sqrt{\mathrm{x}-2}$

Accepted Answer

A)  $\{2,38\}$ 
B)  $\{-2\}$ 
C)  $\{3,8\}$. 
D)  $\{2\}$. 
A)  $\{2,38\}$ 
B)  $\{-2\}$ 
C)  $\{3,8\}$. 
D)  $\{2\}$.

Question 6

Solve by extracting square roots
-$\mathrm{x}^{2}-64=0$

Accepted Answer

A)  $\{34\}$ 
B)  $\{8,-8\}$ 
C)  $\{7,-7\}$ 
D)  $\{8\}$ 
A)  $\{34\}$ 
B)  $\{8,-8\}$ 
C)  $\{7,-7\}$ 
D)  $\{8\}$

Question 7

Determine a quadratic function that results when applying the given shifts to the graph of $f(x)=x^{2}$.
-Rotate about the $x$ - axis, shift 5 units to the right and 16 units up.

Accepted Answer

A)  $f(x)=-(x-5)^{2}+16$ 
B)  $f(x)=(-x-5)^{2}+16$ 
C)  $f(x)=-(x+5)^{2}+16$ 
D)  $f(x)=(-x+5)^{2}+16$ 
A)  $f(x)=-(x-5)^{2}+16$ 
B)  $f(x)=(-x-5)^{2}+16$ 
C)  $f(x)=-(x+5)^{2}+16$ 
D)  $f(x)=(-x+5)^{2}+16$

Question 8

A ladder is resting against a wall. The top of the ladder touches the wall at a height of $6 \mathrm{ft}$. Find the length of the ladder if the length is $2 \mathrm{ft}$ more than its distance from the wall.

Accepted Answer

A)  $8 \mathrm{ft}$ 
B)  $10 \mathrm{ft}$ 
C)  $6 \mathrm{ft}$ 
D)  $12 \mathrm{ft}$ 
A)  $8 \mathrm{ft}$ 
B)  $10 \mathrm{ft}$ 
C)  $6 \mathrm{ft}$ 
D)  $12 \mathrm{ft}$

Question 9

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value.
-$f(x)=6 x^{2}-96 x+385$

Accepted Answer

A)  Maximum, 8 
B)  Maximum, 1 
C)  Minimum, 8 
D)  Minimum, 1 
A)  Maximum, 8 
B)  Maximum, 1 
C)  Minimum, 8 
D)  Minimum, 1

Question 10

Find a quadratic equation with integer coefficients that has the given solution set.
-$\{6,-6\}$

Accepted Answer

A)  $x^{2}-12 x+36=0$ 
B)  $x^{2}+36=0$ 
C)  $x^{2}+12 x+36=0$ 
D)  $x^{2}-36=0$ 
A)  $x^{2}-12 x+36=0$ 
B)  $x^{2}+36=0$ 
C)  $x^{2}+12 x+36=0$ 
D)  $x^{2}-36=0$

Question 11

Approximate to the nearest tenth when necessary.
-The distance $d$, in feet, that a free- falling object falls in $t$ seconds is given by the formula $d=16 t^{2}$. Find the time that it takes for an object to fall 96 feet.

Accepted Answer

A)  2.7 seconds 
B)  2.4 seconds 
C)  39.4 seoonds 
D)  39.2 seconds 
A)  2.7 seconds 
B)  2.4 seconds 
C)  39.4 seoonds 
D)  39.2 seconds

Question 12

Solve the quadratic inequality. Express your solution on a number line using interval notation.
-$x^{2}+5 x \leq-6$

Accepted Answer

A)  $ (2,3) $
  
B)  $ [-3,-2] $
  
C)  $ [2,3] $
  
D)  $ (-\infty, 2] \cup[3, \infty) $
  
A)  $ (2,3) $
  
B)  $ [-3,-2] $
  
C)  $ [2,3] $
  
D)  $ (-\infty, 2] \cup[3, \infty) $

Question 13

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."
-$y=x^{2}+7 x$

Accepted Answer

A)  $(0,0),(7,0)$ 
B)  No intercepts 
C)  $(0,0),(-7,0)$ 
D)  $(0,-7),(-7,0),(0,0)$ 
A)  $(0,0),(7,0)$ 
B)  No intercepts 
C)  $(0,0),(-7,0)$ 
D)  $(0,-7),(-7,0),(0,0)$

Question 14

Solve the equation.
-$1+\frac{1}{\mathrm{x}}=\frac{12}{\mathrm{x}^{2}}$

Accepted Answer

A)  $\{-4,3\}$ 
B)  $\{4,3\}$. 
C)  $\left\{-\frac{1}{4}, \frac{1}{3}\right\}$ 
D)  $\{4,-3\}$ 
A)  $\{-4,3\}$ 
B)  $\{4,3\}$. 
C)  $\left\{-\frac{1}{4}, \frac{1}{3}\right\}$ 
D)  $\{4,-3\}$

Question 15

Solve the equation by completing the square
-$\mathrm{x}^{2}+4 \mathrm{x}=3$

Accepted Answer

A)  $\{-2 \pm 2 \sqrt{7}\}$ 
B)  $\{2+\sqrt{7}\}$ 
C)  $\{-2 \pm \sqrt{7}\}$ 
D)  $\{-1 \pm \sqrt{7}\}$ 
A)  $\{-2 \pm 2 \sqrt{7}\}$ 
B)  $\{2+\sqrt{7}\}$ 
C)  $\{-2 \pm \sqrt{7}\}$ 
D)  $\{-1 \pm \sqrt{7}\}$

Question 16

Solve by using the quadratic formula
-$x^{2}+21 x+110=0$

Accepted Answer

A)  $\{-10,-11\}$ 
B)  $\{10,11\}$ 
C)  $\{-110,-1\}$ 
D)  $\{1,110\}$ 
A)  $\{-10,-11\}$ 
B)  $\{10,11\}$ 
C)  $\{-110,-1\}$ 
D)  $\{1,110\}$

Question 17

Graph the function, and state its domain and range
-$ f(x)=-\sqrt{x}+2 $

Accepted Answer

A)  Domain: $ [-2, \infty) $; Range: $ (-\infty, 0] $
  
B)  Domain: $ [2, \infty) $; Range: $ (-\infty, 0] $
  
C)  Domain: $ [0, \infty) $; Range: $ (-\infty,-2] $
  
D)  Domain: $ [0, \infty) $; Range: $ (-\infty, 2] $
  
A)  Domain: $ [-2, \infty) $; Range: $ (-\infty, 0] $
  
B)  Domain: $ [2, \infty) $; Range: $ (-\infty, 0] $
  
C)  Domain: $ [0, \infty) $; Range: $ (-\infty,-2] $
  
D)  Domain: $ [0, \infty) $; Range: $ (-\infty, 2] $

Question 18

Solve the equation by completing the square
-$x^{2}+3 x=40$

Accepted Answer

A)  $\{8,5\}$ 
B)  $\{-8,-5\}$ 
C)  $\{-8,5\}$. 
D)  $\{-5,8\}$ 
A)  $\{8,5\}$ 
B)  $\{-8,-5\}$ 
C)  $\{-8,5\}$. 
D)  $\{-5,8\}$

Question 19

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^{2}+12 x+36$

Accepted Answer

A)  $(6,0),(0,36)$ 
B)  $(36,0),(0,6)$ 
C)  $(-6,0),(0,36)$ 
D)  $(36,0),(0,-6)$ 
A)  $(6,0),(0,36)$ 
B)  $(36,0),(0,6)$ 
C)  $(-6,0),(0,36)$ 
D)  $(36,0),(0,-6)$

Question 20

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value.
-$f(x)=-x^{2}+16 x-71$

Accepted Answer

A)  Maximum, -7 
B)  Minimum, 8 
C)  Minimum, 7 
D)  Maximum, - 8 
A)  Maximum, -7 
B)  Minimum, 8 
C)  Minimum, 7 
D)  Maximum, - 8

Solve by making a u-substitution - $x^{4}-33 x^{2}+32=0$

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - $f(x)=(x-2)^{2}+2$

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - $(6 \mathrm{x}+9)^{2}=16$

Solve the equation. - $\sqrt{2 \mathrm{x}+5}=3+\sqrt{\mathrm{x}-2}$

Solve by extracting square roots - $\mathrm{x}^{2}-64=0$

Determine a quadratic function that results when applying the given shifts to the graph of $f(x)=x^{2}$ . -Rotate about the $x$ - axis, shift 5 units to the right and 16 units up.

A ladder is resting against a wall. The top of the ladder touches the wall at a height of $6 \mathrm{ft}$ . Find the length of the ladder if the length is $2 \mathrm{ft}$ more than its distance from the wall.

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - $f(x)=6 x^{2}-96 x+385$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{6,-6\}$

Approximate to the nearest tenth when necessary. -The distance $d$ , in feet, that a free- falling object falls in $t$ seconds is given by the formula $d=16 t^{2}$ . Find the time that it takes for an object to fall 96 feet.

Solve the quadratic inequality. Express your solution on a number line using interval notation. - $x^{2}+5 x \leq-6$ $Solve the quadratic inequality. Express your solution on a number line using interval notation. - x^{2}+5 x \leq-6$

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." - $y=x^{2}+7 x$

Solve the equation. - $1+\frac{1}{\mathrm{x}}=\frac{12}{\mathrm{x}^{2}}$

Solve the equation by completing the square - $\mathrm{x}^{2}+4 \mathrm{x}=3$

Solve by using the quadratic formula - $x^{2}+21 x+110=0$

Graph the function, and state its domain and range - $f(x)=-\sqrt{x}+2$ $Graph the function, and state its domain and range - f(x)=-\sqrt{x}+2$

Solve the equation by completing the square - $x^{2}+3 x=40$

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." - $y=x^{2}+12 x+36$

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - $f(x)=-x^{2}+16 x-71$

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 making a u-substitution - x4−33x2+32=0x^{4}-33 x^{2}+32=0x4−33x2+32=0

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - f(x)=(x−2)2+2f(x)=(x-2)^{2}+2f(x)=(x−2)2+2

Solve the quadratic equation using the most efficient technique (factoring, extracting square roots, completing the square, or the quadratic formula). - (6x+9)2=16(6 \mathrm{x}+9)^{2}=16(6x+9)2=16

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 . -

Solve the equation. - 2x+5=3+x−2\sqrt{2 \mathrm{x}+5}=3+\sqrt{\mathrm{x}-2}2x+5​=3+x−2​

Solve by extracting square roots - x2−64=0\mathrm{x}^{2}-64=0x2−64=0

Determine a quadratic function that results when applying the given shifts to the graph of f(x)=x2f(x)=x^{2}f(x)=x2 . -Rotate about the xxx - axis, shift 5 units to the right and 16 units up.

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6ft6 \mathrm{ft}6ft . Find the length of the ladder if the length is 2ft2 \mathrm{ft}2ft more than its distance from the wall.

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - f(x)=6x2−96x+385f(x)=6 x^{2}-96 x+385f(x)=6x2−96x+385

Find a quadratic equation with integer coefficients that has the given solution set. - {6,−6}\{6,-6\}{6,−6}

Approximate to the nearest tenth when necessary. -The distance ddd , in feet, that a free- falling object falls in ttt seconds is given by the formula d=16t2d=16 t^{2}d=16t2 . Find the time that it takes for an object to fall 96 feet.

Solve the quadratic inequality. Express your solution on a number line using interval notation. - x2+5x≤−6x^{2}+5 x \leq-6x2+5x≤−6

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=x2+7xy=x^{2}+7 xy=x2+7x

Solve the equation. - 1+1x=12x21+\frac{1}{\mathrm{x}}=\frac{12}{\mathrm{x}^{2}}1+x1​=x212​

Solve the equation by completing the square - x2+4x=3\mathrm{x}^{2}+4 \mathrm{x}=3x2+4x=3

Solve by using the quadratic formula - x2+21x+110=0x^{2}+21 x+110=0x2+21x+110=0

Graph the function, and state its domain and range - f(x)=−x+2 f(x)=-\sqrt{x}+2 f(x)=−x​+2

Solve the equation by completing the square - x2+3x=40x^{2}+3 x=40x2+3x=40

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=x2+12x+36 y=x^{2}+12 x+36y=x2+12x+36

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - f(x)=−x2+16x−71f(x)=-x^{2}+16 x-71f(x)=−x2+16x−71