Question 1

Solve by using the quadratic formula
-$\mathrm{x}^{2}-25=0$

Accepted Answer

A)  $\{-5\}$ 
B)  $\{-5,0,5\}$ 
C)  $\{5\}$ 
D)  $\{-5,5\}$ 
A)  $\{-5\}$ 
B)  $\{-5,0,5\}$ 
C)  $\{5\}$ 
D)  $\{-5,5\}$

Question 2

Find the vertex
-$f(x)=2 x^{2}-20 x+47$

Accepted Answer

A)  $(-3,5)$ 
B)  $(5,-3)$ 
C)  $(3,-5)$ 
D)  $(-5,3)$ 
A)  $(-3,5)$ 
B)  $(5,-3)$ 
C)  $(3,-5)$ 
D)  $(-5,3)$

Question 3

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

Accepted Answer

A)  $x=-4$ 
B)  $x=3$ 
C)  $x=-3$ 
D)  $x=4$ 
A)  $x=-4$ 
B)  $x=3$ 
C)  $x=-3$ 
D)  $x=4$

Question 4

Solve the quadratic inequality. Express your solution on a number line using interval notation.
-$\mathrm{x}^{2}-2 \mathrm{x}-15<0$

Accepted Answer

A)  $ (-\infty,-3) \cup(5, \infty) $
  
B)  $ (-3,5) $
  
C)  $ (5, \infty) $
  
D)  $ (-\infty,-3) $
  
A)  $ (-\infty,-3) \cup(5, \infty) $
  
B)  $ (-3,5) $
  
C)  $ (5, \infty) $
  
D)  $ (-\infty,-3) $

Question 5

Approximate to the nearest tenth when necessary.
-The area of a square is 100 square centimeters. Find the length of a side of the square.

Accepted Answer

A)  $25 \mathrm{~cm}$ 
B)  $50 \mathrm{~cm}$ 
C)  $10 \mathrm{~cm}$ 
D)  $20 \mathrm{~cm}$ 
A)  $25 \mathrm{~cm}$ 
B)  $50 \mathrm{~cm}$ 
C)  $10 \mathrm{~cm}$ 
D)  $20 \mathrm{~cm}$

Question 6

Solve the polynomial inequality. Express your solution on a number line using interval notation.
-$(x-9)^{3}(x+3)^{2}(x-3) \geq 0$

Accepted Answer

A)  $ [3,9] $
  
B)  $ (-\infty, 3] \cup[9, \infty) $
  
C)  $ (-\infty,-3] \cup[9, \infty) $
  
D)  $ [-3,9] $
  
A)  $ [3,9] $
  
B)  $ (-\infty, 3] \cup[9, \infty) $
  
C)  $ (-\infty,-3] \cup[9, \infty) $
  
D)  $ [-3,9] $

Question 7

Find the $x$ - and $y$-intercepts. If no $x$-intercepts exist, state so.
-$f(x)=x^{2}+11 x$

Accepted Answer

A)  $(0,0),(-11,0)$ 
B)  $(0,-11,(-11,0),(0,0)$ 
C)  $(0,0)$ 
D)  $(0,0),(11,0)$ 
A)  $(0,0),(-11,0)$ 
B)  $(0,-11,(-11,0),(0,0)$ 
C)  $(0,0)$ 
D)  $(0,0),(11,0)$

Question 8

A triangle is $3 \mathrm{~cm}$ wider than it is tall. The area is $27 \mathrm{~cm}^{2}$. Find the base of the triangle.

Accepted Answer

A)  $9 \mathrm{~cm}$ 
B)  $6 \mathrm{~cm}$ 
C)  $3 \mathrm{~cm}$ 
D)  $10 \mathrm{~cm}$ 
A)  $9 \mathrm{~cm}$ 
B)  $6 \mathrm{~cm}$ 
C)  $3 \mathrm{~cm}$ 
D)  $10 \mathrm{~cm}$

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.
-$x^{2}-\frac{2}{3} x$

Accepted Answer

A)  $\frac{1}{9} ;\left(x+\frac{1}{3}\right)^{2}$ 
B)  $-\frac{2}{3} x ;\left(x-\frac{1}{3}\right)^{2}$ 
C)  $9 ;\left(x-\frac{1}{3}\right)^{2}$ 
D)  $\frac{1}{9} ;\left(x-\frac{1}{3}\right)^{2}$ 
A)  $\frac{1}{9} ;\left(x+\frac{1}{3}\right)^{2}$ 
B)  $-\frac{2}{3} x ;\left(x-\frac{1}{3}\right)^{2}$ 
C)  $9 ;\left(x-\frac{1}{3}\right)^{2}$ 
D)  $\frac{1}{9} ;\left(x-\frac{1}{3}\right)^{2}$

Question 10

Solve the polynomial inequality. Express your solution on a number line using interval notation.
-$(x+1)(x-1)(x-5)>0$

Accepted Answer

A)  $ (5, \infty) $
  
B)  $ (-\infty,-1) \cup(1,5) $
  
C)  $ (-\infty, 1) $
  
D)  $ (-1,1) \cup(5, \infty) $
  
A)  $ (5, \infty) $
  
B)  $ (-\infty,-1) \cup(1,5) $
  
C)  $ (-\infty, 1) $
  
D)  $ (-1,1) \cup(5, \infty) $

Question 11

The width of a rectangular computer screen is 2 inches more than its height. If the area of the screen is 195 square inches, find its dimensions.

Accepted Answer

A)  $12 \mathrm{in.}$. by $16 \mathrm{in}$. 
B)  $14 \mathrm{in.}$ by $14 \mathrm{in}$. 
C)  $26 \mathrm{in}$ by $7.5 \mathrm{in}$. 
D)  $13 \mathrm{in}$. by $15 \mathrm{in}$. 
A)  $12 \mathrm{in.}$. by $16 \mathrm{in}$. 
B)  $14 \mathrm{in.}$ by $14 \mathrm{in}$. 
C)  $26 \mathrm{in}$ by $7.5 \mathrm{in}$. 
D)  $13 \mathrm{in}$. by $15 \mathrm{in}$.

Question 12

Find a quadratic equation with integer coefficients that has the given solution set.
-$\{8,-5\}$

Accepted Answer

A)  $x^{2}-40 x-3=0$ 
B)  $x^{2}+3 x-40=0$ 
C)  $x^{2}-3 x-40=0$ 
D)  $x^{2}-40 x+3=0$ 
A)  $x^{2}-40 x-3=0$ 
B)  $x^{2}+3 x-40=0$ 
C)  $x^{2}-3 x-40=0$ 
D)  $x^{2}-40 x+3=0$

Question 13

Find the vertex
-$f(x)=-x^{2}+6 x-14$

Accepted Answer

A)  $(3,5)$ 
B)  $(-3,-5)$ 
C)  $(5,-3)$ 
D)  $(3,-5)$ 
A)  $(3,5)$ 
B)  $(-3,-5)$ 
C)  $(5,-3)$ 
D)  $(3,-5)$

Question 14

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

Accepted Answer

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

Question 15

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

Accepted Answer

A)  Domain: $ [0, \infty) $; Range: $ (-\infty, 5] $
  
B)  Domain: $ [5, \infty) $; Range: $ (-\infty, 0] $
  
C)  Domain: $ [-5, \infty) $; Range: $ (-\infty, 0] $
  
D)  Domain: $ [0, \infty) $; Range: $ (-\infty,-5] $
  
A)  Domain: $ [0, \infty) $; Range: $ (-\infty, 5] $
  
B)  Domain: $ [5, \infty) $; Range: $ (-\infty, 0] $
  
C)  Domain: $ [-5, \infty) $; Range: $ (-\infty, 0] $
  
D)  Domain: $ [0, \infty) $; Range: $ (-\infty,-5] $

Question 16

Solve the quadratic inequality. Express your solution on a number line using interval notation.
-$x^{2}-8 x+7>0$

Accepted Answer

A)  $ (-\infty, 1) $
  
B)  $ (-\infty, 1) \cup(7, \infty) $
  
C)  $ (7, \infty) $
  
D)  $ (1,7) $
  
A)  $ (-\infty, 1) $
  
B)  $ (-\infty, 1) \cup(7, \infty) $
  
C)  $ (7, \infty) $
  
D)  $ (1,7) $

Question 17

Solve the rational inequality. Express your solution on a number line using interval notation.
-$\frac{x-9}{x+1}<0$

Accepted Answer

A)  $(-\infty,-1)$ 
  
B)  $(-\infty,-1)$ or $(9, \infty)$
  
C)  $(-1,9)$
  
D)  $(9, \infty)$
  
A)  $(-\infty,-1)$ 
  
B)  $(-\infty,-1)$ or $(9, \infty)$
  
C)  $(-1,9)$
  
D)  $(9, \infty)$

Question 18

For the given quadratic equation, use the discriminant to determine the number and type of solutions.
-$x^{2}-6 x+5=0$

Accepted Answer

A)  One real 
B)  Two nonreal complex 
C)  Two real 
A)  One real 
B)  Two nonreal complex 
C)  Two real

Question 19

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

Accepted Answer

A)  Domain: $ [0, \infty) $; Range: $ [5, \infty) $
  
B)  Domain: $ [0, \infty) $; Range: $ [-5, \infty) $
  
C)  Domain: $ [-5, \infty) $; Range: $ [0, \infty) $
  
D)  Domain: $ [5, \infty) $; Range: $ [0, \infty) $
  
A)  Domain: $ [0, \infty) $; Range: $ [5, \infty) $
  
B)  Domain: $ [0, \infty) $; Range: $ [-5, \infty) $
  
C)  Domain: $ [-5, \infty) $; Range: $ [0, \infty) $
  
D)  Domain: $ [5, \infty) $; Range: $ [0, \infty) $

Question 20

Determine a quadratic function that results when applying the given shifts to the graph of $f(x)=x^{2}$.
-Shift 5 units to the right.

Accepted Answer

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

Solve by using the quadratic formula - $\mathrm{x}^{2}-25=0$

Find the vertex - $f(x)=2 x^{2}-20 x+47$

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

Solve the quadratic inequality. Express your solution on a number line using interval notation. - $\mathrm{x}^{2}-2 \mathrm{x}-15<0$ $Solve the quadratic inequality. Express your solution on a number line using interval notation. - \mathrm{x}^{2}-2 \mathrm{x}-15<0$

Approximate to the nearest tenth when necessary. -The area of a square is 100 square centimeters. Find the length of a side of the square.

Solve the polynomial inequality. Express your solution on a number line using interval notation. - $(x-9)^{3}(x+3)^{2}(x-3) \geq 0$ $Solve the polynomial inequality. Express your solution on a number line using interval notation. - (x-9)^{3}(x+3)^{2}(x-3) \geq 0$

Find the $x$ - and $y$ -intercepts. If no $x$ -intercepts exist, state so. - $f(x)=x^{2}+11 x$

A triangle is $3 \mathrm{~cm}$ wider than it is tall. The area is $27 \mathrm{~cm}^{2}$ . Find the base of the triangle. $A triangle is 3 \mathrm{~cm} wider than it is tall. The area is 27 \mathrm{~cm}^{2} . Find the base of the triangle.$

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. - $x^{2}-\frac{2}{3} x$

Solve the polynomial inequality. Express your solution on a number line using interval notation. - $(x+1)(x-1)(x-5)>0$

The width of a rectangular computer screen is 2 inches more than its height. If the area of the screen is 195 square inches, find its dimensions.

Find a quadratic equation with integer coefficients that has the given solution set. - $\{8,-5\}$

Find the vertex - $f(x)=-x^{2}+6 x-14$

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

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

Solve the quadratic inequality. Express your solution on a number line using interval notation. - $x^{2}-8 x+7>0$ $Solve the quadratic inequality. Express your solution on a number line using interval notation. - x^{2}-8 x+7>0$

Solve the rational inequality. Express your solution on a number line using interval notation. - $\frac{x-9}{x+1}<0$ $Solve the rational inequality. Express your solution on a number line using interval notation. - \frac{x-9}{x+1}<0$

For the given quadratic equation, use the discriminant to determine the number and type of solutions. - $x^{2}-6 x+5=0$

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

Determine a quadratic function that results when applying the given shifts to the graph of $f(x)=x^{2}$ . -Shift 5 units to the right.

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 using the quadratic formula - x2−25=0\mathrm{x}^{2}-25=0x2−25=0

Find the vertex - f(x)=2x2−20x+47f(x)=2 x^{2}-20 x+47f(x)=2x2−20x+47

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

Solve the quadratic inequality. Express your solution on a number line using interval notation. - x2−2x−15<0\mathrm{x}^{2}-2 \mathrm{x}-15<0x2−2x−15<0

Approximate to the nearest tenth when necessary. -The area of a square is 100 square centimeters. Find the length of a side of the square.

Solve the polynomial inequality. Express your solution on a number line using interval notation. - (x−9)3(x+3)2(x−3)≥0(x-9)^{3}(x+3)^{2}(x-3) \geq 0(x−9)3(x+3)2(x−3)≥0

Find the xxx - and yyy -intercepts. If no xxx -intercepts exist, state so. - f(x)=x2+11xf(x)=x^{2}+11 xf(x)=x2+11x

A triangle is 3 cm3 \mathrm{~cm}3 cm wider than it is tall. The area is 27 cm227 \mathrm{~cm}^{2}27 cm2 . Find the base of the triangle.

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. - x2−23xx^{2}-\frac{2}{3} xx2−32​x

Solve the polynomial inequality. Express your solution on a number line using interval notation. - (x+1)(x−1)(x−5)>0(x+1)(x-1)(x-5)>0(x+1)(x−1)(x−5)>0

The width of a rectangular computer screen is 2 inches more than its height. If the area of the screen is 195 square inches, find its dimensions.

Find a quadratic equation with integer coefficients that has the given solution set. - {8,−5}\{8,-5\}{8,−5}

Find the vertex - f(x)=−x2+6x−14f(x)=-x^{2}+6 x-14f(x)=−x2+6x−14

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

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

Solve the quadratic inequality. Express your solution on a number line using interval notation. - x2−8x+7>0x^{2}-8 x+7>0x2−8x+7>0

Solve the rational inequality. Express your solution on a number line using interval notation. - x−9x+1<0\frac{x-9}{x+1}<0x+1x−9​<0

For the given quadratic equation, use the discriminant to determine the number and type of solutions. - x2−6x+5=0x^{2}-6 x+5=0x2−6x+5=0

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

Determine a quadratic function that results when applying the given shifts to the graph of f(x)=x2f(x)=x^{2}f(x)=x2 . -Shift 5 units to the right.

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 using the quadratic formula - $\mathrm{x}^{2}-25=0$

Find the vertex - $f(x)=2 x^{2}-20 x+47$

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

Solve the quadratic inequality. Express your solution on a number line using interval notation. - $\mathrm{x}^{2}-2 \mathrm{x}-15<0$ $Solve the quadratic inequality. Express your solution on a number line using interval notation. - \mathrm{x}^{2}-2 \mathrm{x}-15<0$

Solve the polynomial inequality. Express your solution on a number line using interval notation. - $(x-9)^{3}(x+3)^{2}(x-3) \geq 0$ $Solve the polynomial inequality. Express your solution on a number line using interval notation. - (x-9)^{3}(x+3)^{2}(x-3) \geq 0$

Find the $x$ - and $y$ -intercepts. If no $x$ -intercepts exist, state so. - $f(x)=x^{2}+11 x$

A triangle is $3 \mathrm{~cm}$ wider than it is tall. The area is $27 \mathrm{~cm}^{2}$ . Find the base of the triangle. $A triangle is 3 \mathrm{~cm} wider than it is tall. The area is 27 \mathrm{~cm}^{2} . Find the base of the triangle.$

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. - $x^{2}-\frac{2}{3} x$

Solve the polynomial inequality. Express your solution on a number line using interval notation. - $(x+1)(x-1)(x-5)>0$

Find a quadratic equation with integer coefficients that has the given solution set. - $\{8,-5\}$

Find the vertex - $f(x)=-x^{2}+6 x-14$

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

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

Solve the quadratic inequality. Express your solution on a number line using interval notation. - $x^{2}-8 x+7>0$ $Solve the quadratic inequality. Express your solution on a number line using interval notation. - x^{2}-8 x+7>0$

Solve the rational inequality. Express your solution on a number line using interval notation. - $\frac{x-9}{x+1}<0$ $Solve the rational inequality. Express your solution on a number line using interval notation. - \frac{x-9}{x+1}<0$

For the given quadratic equation, use the discriminant to determine the number and type of solutions. - $x^{2}-6 x+5=0$

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

Determine a quadratic function that results when applying the given shifts to the graph of $f(x)=x^{2}$ . -Shift 5 units to the right.