Question 1

Graph the function, and state its domain and range
-$ f(x)=(x-5)^{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 2

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

Accepted Answer

A)  No $x$ - intercepts, $(0,10)$ 
B)  $\left(\frac{3 \pm \sqrt{49}}{2}, 0\right),(0,10)$ 
C)  $\left(\frac{3 \pm \sqrt{49}}{2}, 0\right),(0,-10)$ 
D)  No x-intercepts, (0, - 10) 
A)  No $x$ - intercepts, $(0,10)$ 
B)  $\left(\frac{3 \pm \sqrt{49}}{2}, 0\right),(0,10)$ 
C)  $\left(\frac{3 \pm \sqrt{49}}{2}, 0\right),(0,-10)$ 
D)  No x-intercepts, (0, - 10)

Question 3

Graph the given parabola.
-y = -x2 - 4x + 5

Accepted Answer

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

Question 4

Solve the polynomial inequality. Express your solution on a number line using interval notation.
-$(x+7)(x+6)(x+3)<0$

Accepted Answer

A)  $ (-7,-6) \cup(-3, \infty) $
  
B)  $ (-3, \infty) $
  
C)  $ (-\infty,-7) \cup(-6,-3) $
  
D)  $ (-\infty,-6) $
  
A)  $ (-7,-6) \cup(-3, \infty) $
  
B)  $ (-3, \infty) $
  
C)  $ (-\infty,-7) \cup(-6,-3) $
  
D)  $ (-\infty,-6) $

Question 5

A projectile is thrown upward so that its distance (in feet) above the ground after $t$ seconds is given by $h(t)=-14 t^{2}+616 t$. What is its maximum height?

Accepted Answer

A)  $24,200 \mathrm{ft}$ 
B)  $347,424 \mathrm{ft}$ 
C)  $6776 \mathrm{ft}$ 
D)  $8428 \mathrm{ft}$ 
A)  $24,200 \mathrm{ft}$ 
B)  $347,424 \mathrm{ft}$ 
C)  $6776 \mathrm{ft}$ 
D)  $8428 \mathrm{ft}$

Question 6

Graph the given parabola.
-y = -x2 - 4

Accepted Answer

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

Question 7

Approximate to the nearest tenth when necessary.
-The area of a square is 185 square meters. Find the length of a side of the square.

Accepted Answer

A)  $13.6 \mathrm{~m}$ 
B)  $46.3 \mathrm{~m}$ 
C)  $19.2 \mathrm{~m}$ 
D)  $92.5 \mathrm{~m}$ 
A)  $13.6 \mathrm{~m}$ 
B)  $46.3 \mathrm{~m}$ 
C)  $19.2 \mathrm{~m}$ 
D)  $92.5 \mathrm{~m}$

Question 8

A flare is fired from the bottom of a gorge with an initial velocity of 144 feet per second, and it is visible only when the flare is above the rim. The height of the flare, in feet, after $t$ seconds is given by the function $h(t)=-16 t^{2}+144 t$. If the gorge is 288 feet deep, for what length of time can the flare be seen?

Accepted Answer

A)  $6 \mathrm{sec}$ to $9 \mathrm{sec}$ 
B)  $3 \mathrm{sec}$ to $6 \mathrm{sec}$ 
C)  $0 \mathrm{sec}$ to $3 \mathrm{sec}$ 
D)  $9 \mathrm{sec}$ to $12 \mathrm{sec}$ 
A)  $6 \mathrm{sec}$ to $9 \mathrm{sec}$ 
B)  $3 \mathrm{sec}$ to $6 \mathrm{sec}$ 
C)  $0 \mathrm{sec}$ to $3 \mathrm{sec}$ 
D)  $9 \mathrm{sec}$ to $12 \mathrm{sec}$

Question 9

Find the vertex of the parabola associated with the quadratic equation.
-$y=x^{2}-6 x+18$

Accepted Answer

A)  $(9,0)$ 
B)  $(0,3)$ 
C)  $(9,3)$ 
D)  $(3,9)$ 
A)  $(9,0)$ 
B)  $(0,3)$ 
C)  $(9,3)$ 
D)  $(3,9)$

Question 10

Round your answer to the nearest tenth, when appropriate.

-A toy rocket is shot vertically upward from the ground. Its distanœe in feet from the ground in $t$ seconds is given by $h(t)=-16 t^{2}+133 t$. At what time or times will the ball be 146 feet from the ground?

Accepted Answer

A)  $8.3 \mathrm{sec}$ 
B)  $129.1 \mathrm{sec}, 136.9 \mathrm{sec}$ 
C)  $1.3 \mathrm{sec}, 7 \mathrm{sec}$ 
D)  $4.2 \mathrm{sec}$ 
A)  $8.3 \mathrm{sec}$ 
B)  $129.1 \mathrm{sec}, 136.9 \mathrm{sec}$ 
C)  $1.3 \mathrm{sec}, 7 \mathrm{sec}$ 
D)  $4.2 \mathrm{sec}$

Question 11

Graph the function, and state its domain and range
-$ f(x)=-\sqrt{x+5}+6 $

Accepted Answer

A)  Domain: $ [-5, \infty) $; Range: $ (-\infty,-6] $
  
B)  Domain: $ [5, \infty) $; Range: $ (-\infty, 6] $
  
C)  Domain: $ [-5, \infty) $; Range: $ (-\infty, 6] $
  
D)  Domain: $ [5, \infty) $; Range: $ (-\infty,-6] $
  
A)  Domain: $ [-5, \infty) $; Range: $ (-\infty,-6] $
  
B)  Domain: $ [5, \infty) $; Range: $ (-\infty, 6] $
  
C)  Domain: $ [-5, \infty) $; Range: $ (-\infty, 6] $
  
D)  Domain: $ [5, \infty) $; Range: $ (-\infty,-6] $

Question 12

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 13

Given $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-4 \mathrm{x}-21$, find all values for $\mathrm{x}$ for which $\mathrm{f}(\mathrm{x})<0$.

Accepted Answer

A)  $(-\infty,-3) \cup(7, \infty)$ 
B)  $(7, \infty)$ 
C)  $(-\infty,-3)$ 
D)  $(-3,7)$ 
A)  $(-\infty,-3) \cup(7, \infty)$ 
B)  $(7, \infty)$ 
C)  $(-\infty,-3)$ 
D)  $(-3,7)$

Question 14

Graph the given parabola.
-y = x2 - 6x +8

Accepted Answer

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

Question 15

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.
-$x^{2}-\frac{5}{2} x$

Accepted Answer

A)  $\frac{25}{4} ;\left(x-\frac{5}{4}\right)^{2}$ 
B)  $\frac{25}{16} ;\left(x+\frac{5}{4}\right)^{2}$ 
C)  $\frac{25}{16} ;\left(x-\frac{5}{4}\right)^{2}$ 
D)  0 ; $\left(x-\frac{5}{4}\right)^{2}$ 
A)  $\frac{25}{4} ;\left(x-\frac{5}{4}\right)^{2}$ 
B)  $\frac{25}{16} ;\left(x+\frac{5}{4}\right)^{2}$ 
C)  $\frac{25}{16} ;\left(x-\frac{5}{4}\right)^{2}$ 
D)  0 ; $\left(x-\frac{5}{4}\right)^{2}$

Question 16

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

Accepted Answer

A)  left 2 units 
B)  down 2 units 
C)  right 2 units 
D)  up 2 units 
A)  left 2 units 
B)  down 2 units 
C)  right 2 units 
D)  up 2 units

Question 17

Solve the polynomial inequality.  Express your solution on a number line using interval notation.
-Use the graph of $y=x^{3}+4 x^{2}+x-6$ to solve $x^{3}+4 x^{2}+x-6 \leq 0$

Accepted Answer

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

Question 18

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.
-$f(x)=(x-2)^{2}+13$

Accepted Answer

A)  right 13 units, down 2 units 
B)  right 2 units, up 13 units 
C)  rotate about $x$ - axis, right 2 units, up 13 units 
D)  left 2 units, up 13 units 
A)  right 13 units, down 2 units 
B)  right 2 units, up 13 units 
C)  rotate about $x$ - axis, right 2 units, up 13 units 
D)  left 2 units, up 13 units

Question 19

Find a quadratic equation with integer coefficients that has the given solution set.
-$\{0,2\}$

Accepted Answer

A)  $x^{2}-4=0$ 
B)  $x^{2}+2 x=0$ 
C)  $x^{2}-2 x=0$ 
D)  $x^{2}+2 x+4=0$ 
A)  $x^{2}-4=0$ 
B)  $x^{2}+2 x=0$ 
C)  $x^{2}-2 x=0$ 
D)  $x^{2}+2 x+4=0$

Question 20

Find the axis of symmetry associated with the quadratic equation.
-$y=x^{2}-1$

Accepted Answer

A)  $x=6$ 
B)  $x=-1$ 
C)  $x=0$ 
D)  $x=1$ 
A)  $x=6$ 
B)  $x=-1$ 
C)  $x=0$ 
D)  $x=1$

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

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

Graph the given parabola. -y = -x² - 4x + 5

Solve the polynomial inequality. Express your solution on a number line using interval notation. - $(x+7)(x+6)(x+3)<0$

A projectile is thrown upward so that its distance (in feet) above the ground after $t$ seconds is given by $h(t)=-14 t^{2}+616 t$ . What is its maximum height?

Graph the given parabola. -y = -x² - 4

Approximate to the nearest tenth when necessary. -The area of a square is 185 square meters. Find the length of a side of the square.

Find the vertex of the parabola associated with the quadratic equation. - $y=x^{2}-6 x+18$

Round your answer to the nearest tenth, when appropriate. -A toy rocket is shot vertically upward from the ground. Its distanœe in feet from the ground in $t$ seconds is given by $h(t)=-16 t^{2}+133 t$ . At what time or times will the ball be 146 feet from the ground?

Graph the function, and state its domain and range - $f(x)=-\sqrt{x+5}+6$ $Graph the function, and state its domain and range - f(x)=-\sqrt{x+5}+6$

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

Given $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-4 \mathrm{x}-21$ , find all values for $\mathrm{x}$ for which $\mathrm{f}(\mathrm{x})<0$ .

Graph the given parabola. -y = x² - 6x +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. - $x^{2}-\frac{5}{2} x$

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

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. - $f(x)=(x-2)^{2}+13$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{0,2\}$

Find the axis of symmetry associated with the quadratic equation. - $y=x^{2}-1$

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

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

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

Graph the given parabola. -y = -x2 - 4x + 5

Solve the polynomial inequality. Express your solution on a number line using interval notation. - (x+7)(x+6)(x+3)<0(x+7)(x+6)(x+3)<0(x+7)(x+6)(x+3)<0

A projectile is thrown upward so that its distance (in feet) above the ground after ttt seconds is given by h(t)=−14t2+616th(t)=-14 t^{2}+616 th(t)=−14t2+616t . What is its maximum height?

Graph the given parabola. -y = -x2 - 4

Approximate to the nearest tenth when necessary. -The area of a square is 185 square meters. Find the length of a side of the square.

Find the vertex of the parabola associated with the quadratic equation. - y=x2−6x+18y=x^{2}-6 x+18y=x2−6x+18

Graph the function, and state its domain and range - f(x)=−x+5+6 f(x)=-\sqrt{x+5}+6 f(x)=−x+5​+6

Graph the function, and state its domain and range - f(x)=−x3−4 f(x)=-x^{3}-4 f(x)=−x3−4

Given f(x)=x2−4x−21\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-4 \mathrm{x}-21f(x)=x2−4x−21 , find all values for x\mathrm{x}x for which f(x)<0\mathrm{f}(\mathrm{x})<0f(x)<0 .

Graph the given parabola. -y = x2 - 6x +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. - x2−52xx^{2}-\frac{5}{2} xx2−25​x

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)=x2−2f(x)=x^{2}-2f(x)=x2−2

Solve the polynomial inequality. Express your solution on a number line using interval notation. -Use the graph of y=x3+4x2+x−6y=x^{3}+4 x^{2}+x-6y=x3+4x2+x−6 to solve x3+4x2+x−6≤0x^{3}+4 x^{2}+x-6 \leq 0x3+4x2+x−6≤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−2)2+13f(x)=(x-2)^{2}+13f(x)=(x−2)2+13

Find a quadratic equation with integer coefficients that has the given solution set. - {0,2}\{0,2\}{0,2}

Find the axis of symmetry associated with the quadratic equation. - y=x2−1y=x^{2}-1y=x2−1

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

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

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

Graph the given parabola. -y = -x² - 4x + 5

Solve the polynomial inequality. Express your solution on a number line using interval notation. - $(x+7)(x+6)(x+3)<0$

A projectile is thrown upward so that its distance (in feet) above the ground after $t$ seconds is given by $h(t)=-14 t^{2}+616 t$ . What is its maximum height?

Graph the given parabola. -y = -x² - 4

Find the vertex of the parabola associated with the quadratic equation. - $y=x^{2}-6 x+18$

Graph the function, and state its domain and range - $f(x)=-\sqrt{x+5}+6$ $Graph the function, and state its domain and range - f(x)=-\sqrt{x+5}+6$

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

Given $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-4 \mathrm{x}-21$ , find all values for $\mathrm{x}$ for which $\mathrm{f}(\mathrm{x})<0$ .

Graph the given parabola. -y = x² - 6x +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. - $x^{2}-\frac{5}{2} x$

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

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. - $f(x)=(x-2)^{2}+13$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{0,2\}$

Find the axis of symmetry associated with the quadratic equation. - $y=x^{2}-1$