Question 1

A projectile is thrown upward so that its distance above the ground after $t$ sec is given by $h(t)=-15 t^{2}+600 t$. After how many seconds does it reach its maximum height?

Accepted Answer

A)  $10 \mathrm{sec}$ 
B)  $20 \mathrm{sec}$ 
C)  $30 \mathrm{sec}$ 
D)  $40 \mathrm{sec}$ 
A)  $10 \mathrm{sec}$ 
B)  $20 \mathrm{sec}$ 
C)  $30 \mathrm{sec}$ 
D)  $40 \mathrm{sec}$

Question 2

Solve the equation.
-$\mathrm{x}-8=\frac{9}{\mathrm{x}}$

Accepted Answer

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

Question 3

Solve by making a u-substitution
-$(3 m+3)^{2}-12(3 m+3)+35=0$

Accepted Answer

A)  $\left\{\frac{10}{3},-\frac{8}{3}\right\}$ 
B)  $\left\{-\frac{10}{3}, \frac{8}{3}\right\}$ 
C)  $\left\{\frac{4}{3}, \frac{2}{3}\right\}$ 
D)  $\left\{-\frac{4}{3},-\frac{2}{3}\right\}$ 
A)  $\left\{\frac{10}{3},-\frac{8}{3}\right\}$ 
B)  $\left\{-\frac{10}{3}, \frac{8}{3}\right\}$ 
C)  $\left\{\frac{4}{3}, \frac{2}{3}\right\}$ 
D)  $\left\{-\frac{4}{3},-\frac{2}{3}\right\}$

Question 4

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.
-$f(x)=(x+16)^{2}-98$

Accepted Answer

A)  left 16 units, down 98 units 
B)  right 16 units, down 98 units 
C)  right 98 units, up 16 units 
D)  left 98 units, up 16 units 
A)  left 16 units, down 98 units 
B)  right 16 units, down 98 units 
C)  right 98 units, up 16 units 
D)  left 98 units, up 16 units

Question 5

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

Accepted Answer

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

Question 6

Solve by factoring.
-$x^{2}-81=0$

Accepted Answer

A)  $\{9\}$ 
B)  $\{9,0,9\}$ 
C)  $\{9\}$. 
D)  $\{-9,9\}$ 
A)  $\{9\}$ 
B)  $\{9,0,9\}$ 
C)  $\{9\}$. 
D)  $\{-9,9\}$

Question 7

Solve the equation.
-$\frac{8}{x+2}-\frac{4}{x-2}=\frac{8}{x^{2}-4}$

Accepted Answer

A)  $\{28\}$ 
B)  $\{32\}$ 
C)  $\{8\}$ 
D)  $\{-8\}$. 
A)  $\{28\}$ 
B)  $\{32\}$ 
C)  $\{8\}$ 
D)  $\{-8\}$.

Question 8

Find the vertex of the parabola associated with the quadratic equation.
-$y=3 x^{2}+24 x+51$

Accepted Answer

A)  $(3,-4)$ 
B)  $(4,-3)$ 
C)  $(-4,3)$ 
D)  $(-3,4)$ 
A)  $(3,-4)$ 
B)  $(4,-3)$ 
C)  $(-4,3)$ 
D)  $(-3,4)$

Question 9

Find the $x$ - and $y$-intercepts. If no $x$-intercepts exist, state so.
-$f(x)=x^{2}-3 x+8$

Accepted Answer

A)  $\left(\frac{3 \pm \sqrt{41}}{2}, 0\right),(0,-8)$ 
B)  No x- intercepts, (0, - 8) 
C)  $\left(\frac{3 \pm \sqrt{41}}{2}, 0\right),(0,8)$ 
D)  No x-intercepts, (0, 8) 
A)  $\left(\frac{3 \pm \sqrt{41}}{2}, 0\right),(0,-8)$ 
B)  No x- intercepts, (0, - 8) 
C)  $\left(\frac{3 \pm \sqrt{41}}{2}, 0\right),(0,8)$ 
D)  No x-intercepts, (0, 8)

Question 10

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."
-$y=-x^{2}+5 x-6$

Accepted Answer

A)  $(2,0),(3,0),(0,2)$ 
B)  $(2,0),(3,0),(0,-6)$ 
C)  $(-2,0),(-3,0),(0,-6)$ 
D)  No $x$-intercepts, $(0,2)$ 
A)  $(2,0),(3,0),(0,2)$ 
B)  $(2,0),(3,0),(0,-6)$ 
C)  $(-2,0),(-3,0),(0,-6)$ 
D)  No $x$-intercepts, $(0,2)$

Question 11

State the domain and range of the given function
-$f(x)=-(x+8)^{2}-6$

Accepted Answer

A)  Domain: $(-\infty, \infty)$ Range: $(-\infty,-6]$ 
B)  Domain: $(-\infty, \infty)$ Range: $[-6, \infty)$ 
C)  Domain: $(-\infty, \infty)$ Range: $(-\infty, \infty)$ 
D)  Domain: $[8, \infty)$ Range: $(-\infty,-6]$ 
A)  Domain: $(-\infty, \infty)$ Range: $(-\infty,-6]$ 
B)  Domain: $(-\infty, \infty)$ Range: $[-6, \infty)$ 
C)  Domain: $(-\infty, \infty)$ Range: $(-\infty, \infty)$ 
D)  Domain: $[8, \infty)$ Range: $(-\infty,-6]$

Question 12

Approximate to the nearest tenth when necessary.
-The area of a circle is 90 square meters. Find the radius of the circle.

Accepted Answer

A)  $9.5 \mathrm{~m}$ 
B)  $5.4 \mathrm{~m}$ 
C)  $16.8 \mathrm{~m}$ 
D)  $28.6 \mathrm{~m}$ 
A)  $9.5 \mathrm{~m}$ 
B)  $5.4 \mathrm{~m}$ 
C)  $16.8 \mathrm{~m}$ 
D)  $28.6 \mathrm{~m}$

Question 13

Solve the equation by completing the square
-$\mathrm{x}^{2}+90=19 \mathrm{x}$

Accepted Answer

A)  $\{-9,-10\}$ 
B)  $\{-90,-1\}$ 
C)  $\{9,10\}$ 
D)  $\{1,90\}$ 
A)  $\{-9,-10\}$ 
B)  $\{-90,-1\}$ 
C)  $\{9,10\}$ 
D)  $\{1,90\}$

Question 14

Solve the rational inequality. Express your solution on a number line using interval notation.
-$\frac{x-8}{x+9}>0$

Accepted Answer

A)  $ (-\infty,-9) $
  
B)  $ (-\infty,-9) $ or $ (8, \infty) $
  
C)  $ (-9,8) $
  
D)  $ (8, \infty) $
  
A)  $ (-\infty,-9) $
  
B)  $ (-\infty,-9) $ or $ (8, \infty) $
  
C)  $ (-9,8) $
  
D)  $ (8, \infty) $

Question 15

Solve the rational inequality. Express your solution on a number line using interval notation.
-$\frac{(x-1)(3-x)}{(x-2)^{2}} \leq 0$

Accepted Answer

A)  $ (-\infty,-3] \cup(-2,-1) \cup[1, \infty) $
  
B)  $ (-\infty, 1) \cup(3, \infty) $
  
C)  $ (-\infty, 1] \cup[3, \infty) $
  
D)  $ (-\infty,-3) \cup(-1, \infty) $
  
A)  $ (-\infty,-3] \cup(-2,-1) \cup[1, \infty) $
  
B)  $ (-\infty, 1) \cup(3, \infty) $
  
C)  $ (-\infty, 1] \cup[3, \infty) $
  
D)  $ (-\infty,-3) \cup(-1, \infty) $

Question 16

Graph the given parabola.
-$y=x^{2}-4$

Accepted Answer

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

Question 17

Approximate to the nearest tenth when necessary.
-The velocity $\mathrm{v}$, in $\mathrm{ft} / \mathrm{s}$, of a free falling object after $\mathrm{t}$ seconds is given by the formula v $32 \mathrm{t}$ until the object reaches terminal velocity. The terminal velocity $\mathrm{V}_{\mathrm{t}}$ of a free-falling object is the highest velocity that the object can attain, and it depends on the mass of the object as well as its projected area. The distance $d$, in feet, that a free-falling object falls in $t$ seconds is given by the formula $\mathrm{d} e=16 \mathrm{t}^{2}$ until it reaches terminal velocity. After that occurs, the distance that it falls is found by multiplying the terminal velocity $\mathrm{V}_{\mathrm{t}}$ by the amount of time after it reaches terminal velocity. Find the distance that a parachutist travels in $\mathrm{t}=45$ seconds if she has the given terminal velocity $\mathrm{V}_{\mathrm{t}}=16 \mathrm{ft} / \mathrm{s}$.

Accepted Answer

A)  512 feet 
B)  716 feet 
C)  720 feet 
D)  480 feet 
A)  512 feet 
B)  716 feet 
C)  720 feet 
D)  480 feet

Question 18

Solve by factoring.
-$\mathrm{x}^{2}-\mathrm{x}-42=0$

Accepted Answer

A)  $\{7,6\}$ 
B)  $\{6,7\}$ 
C)  $\{-6,-7\}$ 
D)  $\{-6,7\}$ 
A)  $\{7,6\}$ 
B)  $\{6,7\}$ 
C)  $\{-6,-7\}$ 
D)  $\{-6,7\}$

Question 19

Graph the function, and state its domain and range
-$ f(x)=x^{3}-4 $

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 20

Solve by making a u-substitution
-$x^{2 / 3}-2 x^{1 / 3}-15=0$

Accepted Answer

A)  $\{-27,125\}$ 
B)  $\{27,125\}$. 
C)  $\{-27,-125\}$ 
D)  $\{27,-125\}$. 
A)  $\{-27,125\}$ 
B)  $\{27,125\}$. 
C)  $\{-27,-125\}$ 
D)  $\{27,-125\}$.

A projectile is thrown upward so that its distance above the ground after $t$ sec is given by $h(t)=-15 t^{2}+600 t$ . After how many seconds does it reach its maximum height?

Solve the equation. - $\mathrm{x}-8=\frac{9}{\mathrm{x}}$

Solve by making a u-substitution - $(3 m+3)^{2}-12(3 m+3)+35=0$

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. - $f(x)=(x+16)^{2}-98$

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

Solve by factoring. - $x^{2}-81=0$

Solve the equation. - $\frac{8}{x+2}-\frac{4}{x-2}=\frac{8}{x^{2}-4}$

Find the vertex of the parabola associated with the quadratic equation. - $y=3 x^{2}+24 x+51$

Find the $x$ - and $y$ -intercepts. If no $x$ -intercepts exist, state so. - $f(x)=x^{2}-3 x+8$

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." - $y=-x^{2}+5 x-6$

State the domain and range of the given function - $f(x)=-(x+8)^{2}-6$

Approximate to the nearest tenth when necessary. -The area of a circle is 90 square meters. Find the radius of the circle.

Solve the equation by completing the square - $\mathrm{x}^{2}+90=19 \mathrm{x}$

Solve the rational inequality. Express your solution on a number line using interval notation. - $\frac{x-8}{x+9}>0$ $Solve the rational inequality. Express your solution on a number line using interval notation. - \frac{x-8}{x+9}>0$

Solve the rational inequality. Express your solution on a number line using interval notation. - $\frac{(x-1)(3-x)}{(x-2)^{2}} \leq 0$ $Solve the rational inequality. Express your solution on a number line using interval notation. - \frac{(x-1)(3-x)}{(x-2)^{2}} \leq 0$

Graph the given parabola. - $y=x^{2}-4$ $Graph the given parabola. - y=x^{2}-4$

Solve by factoring. - $\mathrm{x}^{2}-\mathrm{x}-42=0$

Graph the function, and state its domain and range - $f(x)=x^{3}-4$ $Graph the function, and state its domain and range - f(x)=x^{3}-4$

Solve by making a u-substitution - $x^{2 / 3}-2 x^{1 / 3}-15=0$

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

A projectile is thrown upward so that its distance above the ground after ttt sec is given by h(t)=−15t2+600th(t)=-15 t^{2}+600 th(t)=−15t2+600t . After how many seconds does it reach its maximum height?

Solve the equation. - x−8=9x\mathrm{x}-8=\frac{9}{\mathrm{x}}x−8=x9​

Solve by making a u-substitution - (3m+3)2−12(3m+3)+35=0(3 m+3)^{2}-12(3 m+3)+35=0(3m+3)2−12(3m+3)+35=0

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+16)2−98f(x)=(x+16)^{2}-98f(x)=(x+16)2−98

Find the vertex - f(x)=(x+6)2−6f(x)=(x+6)^{2}-6f(x)=(x+6)2−6

Solve by factoring. - x2−81=0x^{2}-81=0x2−81=0

Solve the equation. - 8x+2−4x−2=8x2−4\frac{8}{x+2}-\frac{4}{x-2}=\frac{8}{x^{2}-4}x+28​−x−24​=x2−48​

Find the vertex of the parabola associated with the quadratic equation. - y=3x2+24x+51y=3 x^{2}+24 x+51y=3x2+24x+51

Find the xxx - and yyy -intercepts. If no xxx -intercepts exist, state so. - f(x)=x2−3x+8f(x)=x^{2}-3 x+8f(x)=x2−3x+8

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+5x−6y=-x^{2}+5 x-6y=−x2+5x−6

State the domain and range of the given function - f(x)=−(x+8)2−6f(x)=-(x+8)^{2}-6f(x)=−(x+8)2−6