Question 1

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."
-$y=-x^{2}+5 x-19$

Accepted Answer

A)  $\left(\frac{-5 \pm \sqrt{101}}{2}, 0\right),(0,19)$ 
B)  No x-intercepts, (0, 19) 
C)  $\left(\frac{-5 \pm \sqrt{101}}{2}, 0\right),(0,-19)$ 
D)  No x-intercepts, (0, - 19) 
A)  $\left(\frac{-5 \pm \sqrt{101}}{2}, 0\right),(0,19)$ 
B)  No x-intercepts, (0, 19) 
C)  $\left(\frac{-5 \pm \sqrt{101}}{2}, 0\right),(0,-19)$ 
D)  No x-intercepts, (0, - 19)

Question 2

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

Accepted Answer

A)  $0 ;\left(x-\frac{3}{2}\right)^{2}$ 
B)  $\frac{9}{4} ;\left(x-\frac{3}{2}\right)^{2}$ 
C)  $\frac{9}{4} ;\left(x+\frac{3}{2}\right)^{2}$ 
D)  $9 ;(x-3)^{2}$ 
A)  $0 ;\left(x-\frac{3}{2}\right)^{2}$ 
B)  $\frac{9}{4} ;\left(x-\frac{3}{2}\right)^{2}$ 
C)  $\frac{9}{4} ;\left(x+\frac{3}{2}\right)^{2}$ 
D)  $9 ;(x-3)^{2}$

Question 3

Solve the equation.
-$\sqrt{2 x+3}-\sqrt{x+1}=1$

Accepted Answer

A)  $\{3,-1\}$ 
B)  $\{-3,-1\}$. 
C)  $\{3\}$ 
D)  $\varnothing$ 
A)  $\{3,-1\}$ 
B)  $\{-3,-1\}$. 
C)  $\{3\}$ 
D)  $\varnothing$

Question 4

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 and 10 units down.

Accepted Answer

A)  $f(x)=(x+10)^{2}-5$ 
B)  $f(x)=(x-5)^{2}-10$ 
C)  $f(x)=(x-10)^{2}-5$ 
D)  $f(x)=(x+5)^{2}-10$ 
A)  $f(x)=(x+10)^{2}-5$ 
B)  $f(x)=(x-5)^{2}-10$ 
C)  $f(x)=(x-10)^{2}-5$ 
D)  $f(x)=(x+5)^{2}-10$

Question 5

Find the vertex
-$f(x)=(x+1)^{2}+1$

Accepted Answer

A)  $(0,1)$ 
B)  $(-1,-1)$ 
C)  $(-1,1)$ 
D)  $(1,0)$ 
A)  $(0,1)$ 
B)  $(-1,-1)$ 
C)  $(-1,1)$ 
D)  $(1,0)$

Question 6

Find the vertex of the parabola associated with the quadratic equation.
-$y=x^{2}+5$

Accepted Answer

A)  $(5,0)$ 
B)  $(5,5)$ 
C)  $(0,0)$ 
D)  $(0,5)$ 
A)  $(5,0)$ 
B)  $(5,5)$ 
C)  $(0,0)$ 
D)  $(0,5)$

Question 7

Solve by factoring.
-$x^{2}+10 x+24=0$

Accepted Answer

A)  $\{4,-6\}$ 
B)  $\{1,24\}$ 
C)  $\{4,6\}$ 
D)  $\{24,-1\}$ 
A)  $\{4,-6\}$ 
B)  $\{1,24\}$ 
C)  $\{4,6\}$ 
D)  $\{24,-1\}$

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

A lot is in the shape of a right triangle. The shorter leg measures $60 \mathrm{~m}$. The hypotenuse is $20 \mathrm{~m}$ longer than the length of the longer leg. How long is the longer leg?

Accepted Answer

A)  $120 \mathrm{~m}$ 
B)  $100 \mathrm{~m}$ 
C)  $60 \mathrm{~m}$ 
D)  $80 \mathrm{~m}$ 
A)  $120 \mathrm{~m}$ 
B)  $100 \mathrm{~m}$ 
C)  $60 \mathrm{~m}$ 
D)  $80 \mathrm{~m}$

Question 11

Given $f(x)=\frac{x^{2}-3 x-4}{x^{2}+11 x+30}$, find all values for $x$ for which $f(x)<0$.

Accepted Answer

A)  $(-\infty,-4) \cup(1,4) \cup(5, \infty)$ 
B)  $(-1,4)$ 
C)  $(-6,-5) \cup(-1,4)$ 
D)  $(-\infty,-6) \cup(-5,-1) \cup(4, \infty)$ 
A)  $(-\infty,-4) \cup(1,4) \cup(5, \infty)$ 
B)  $(-1,4)$ 
C)  $(-6,-5) \cup(-1,4)$ 
D)  $(-\infty,-6) \cup(-5,-1) \cup(4, \infty)$

Question 12

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value.
-$f(x)=(x+6)^{2}-3$

Accepted Answer

A)  Maximum, -3 
B)  Minimum, 6 
C)  Minimum, - 3 
D)  Maximum, 6 
A)  Maximum, -3 
B)  Minimum, 6 
C)  Minimum, - 3 
D)  Maximum, 6

Question 13

John owns a hot dog stand. He has found that his profit is given by the equation $\mathrm{P}(\mathrm{x})=-\mathrm{x}^{2}+70 \mathrm{x}+82$, where $\mathrm{x}$ is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Accepted Answer

A)  23 hot dogs 
B)  47 hot dogs 
C)  36 hot dogs 
D)  35 hot dogs 
A)  23 hot dogs 
B)  47 hot dogs 
C)  36 hot dogs 
D)  35 hot dogs

Question 14

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value.
-$f(x)=-(x+1)^{2}-2$

Accepted Answer

A)  Maximum, 1 
B)  Minimum, 1 
C)  Maximum, - 2 
D)  Minimum, - 2 
A)  Maximum, 1 
B)  Minimum, 1 
C)  Maximum, - 2 
D)  Minimum, - 2

Question 15

Graph the function, and state its domain and range
-$ f(x)=-(x+4)^{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 16

Given $f(x)=\frac{x-1}{x+5}$, find all values for $x$ for which $f(x)>0$.

Accepted Answer

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

Question 17

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.
-$f(x)=-(x-2)^{2}-4$

Accepted Answer

A)  left 2 units, down 4 units 
B)  rotate about $x$ - axis, left 2 units, down 4 units 
C)  right 2 units, down 4 units 
D)  rotate about $\mathrm{x}$ - axis, right 2 units, down 4 units 
A)  left 2 units, down 4 units 
B)  rotate about $x$ - axis, left 2 units, down 4 units 
C)  right 2 units, down 4 units 
D)  rotate about $\mathrm{x}$ - axis, right 2 units, down 4 units

Question 18

Find the $x$ - and $y$-intercepts. If no $x$-intercepts exist, state so.
-$f(x)=2 x^{2}-12 x-14$

Accepted Answer

A)  $(-7,0),(1,0),(0,-14)$ 
B)  $(-7,0),(-1,0),(0,14)$ 
C)  $(7,0),(-1,0),(0,-14)$ 
D)  $(7,0),(1,0),(0,14)$ 
A)  $(-7,0),(1,0),(0,-14)$ 
B)  $(-7,0),(-1,0),(0,14)$ 
C)  $(7,0),(-1,0),(0,-14)$ 
D)  $(7,0),(1,0),(0,14)$

Question 19

Solve by extracting square roots
-$x^{2}=24$

Accepted Answer

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

Question 20

Find a rational inequality whose solution is given
-

Accepted Answer

A)  $\frac{x-2}{x+7}>0$ 
B)  $\frac{x+2}{x+7}0$ 
A)  $\frac{x-2}{x+7}>0$ 
B)  $\frac{x+2}{x+7}0$

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." - $y=-x^{2}+5 x-19$

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

Solve the equation. - $\sqrt{2 x+3}-\sqrt{x+1}=1$

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 and 10 units down.

Find the vertex - $f(x)=(x+1)^{2}+1$

Find the vertex of the parabola associated with the quadratic equation. - $y=x^{2}+5$

Solve by factoring. - $x^{2}+10 x+24=0$

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

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

A lot is in the shape of a right triangle. The shorter leg measures $60 \mathrm{~m}$ . The hypotenuse is $20 \mathrm{~m}$ longer than the length of the longer leg. How long is the longer leg?

Given $f(x)=\frac{x^{2}-3 x-4}{x^{2}+11 x+30}$ , find all values for $x$ for which $f(x)<0$ .

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - $f(x)=(x+6)^{2}-3$

John owns a hot dog stand. He has found that his profit is given by the equation $\mathrm{P}(\mathrm{x})=-\mathrm{x}^{2}+70 \mathrm{x}+82$ , where $\mathrm{x}$ is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - $f(x)=-(x+1)^{2}-2$

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

Given $f(x)=\frac{x-1}{x+5}$ , find all values for $x$ for which $f(x)>0$ .

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. - $f(x)=-(x-2)^{2}-4$

Find the $x$ - and $y$ -intercepts. If no $x$ -intercepts exist, state so. - $f(x)=2 x^{2}-12 x-14$

Solve by extracting square roots - $x^{2}=24$

Find a rational inequality whose solution is given -

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

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−19y=-x^{2}+5 x-19y=−x2+5x−19

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. - x2−3xx^{2}-3 xx2−3x

Solve the equation. - 2x+3−x+1=1\sqrt{2 x+3}-\sqrt{x+1}=12x+3​−x+1​=1

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 and 10 units down.

Find the vertex - f(x)=(x+1)2+1f(x)=(x+1)^{2}+1f(x)=(x+1)2+1

Find the vertex of the parabola associated with the quadratic equation. - y=x2+5y=x^{2}+5y=x2+5

Solve by factoring. - x2+10x+24=0x^{2}+10 x+24=0x2+10x+24=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 . -Shift 5 units to the left.

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

A lot is in the shape of a right triangle. The shorter leg measures 60 m60 \mathrm{~m}60 m . The hypotenuse is 20 m20 \mathrm{~m}20 m longer than the length of the longer leg. How long is the longer leg?

Given f(x)=x2−3x−4x2+11x+30f(x)=\frac{x^{2}-3 x-4}{x^{2}+11 x+30}f(x)=x2+11x+30x2−3x−4​ , find all values for xxx for which f(x)<0f(x)<0f(x)<0 .

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - f(x)=(x+6)2−3f(x)=(x+6)^{2}-3f(x)=(x+6)2−3

John owns a hot dog stand. He has found that his profit is given by the equation P(x)=−x2+70x+82\mathrm{P}(\mathrm{x})=-\mathrm{x}^{2}+70 \mathrm{x}+82P(x)=−x2+70x+82 , where x\mathrm{x}x is the number of hot dogs sold. How many hot dogs must he sell to earn the most profit?

Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value. - f(x)=−(x+1)2−2f(x)=-(x+1)^{2}-2f(x)=−(x+1)2−2

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

Given f(x)=x−1x+5f(x)=\frac{x-1}{x+5}f(x)=x+5x−1​ , find all values for xxx for which f(x)>0f(x)>0f(x)>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)2−4f(x)=-(x-2)^{2}-4f(x)=−(x−2)2−4

Find the xxx - and yyy -intercepts. If no xxx -intercepts exist, state so. - f(x)=2x2−12x−14f(x)=2 x^{2}-12 x-14f(x)=2x2−12x−14

Solve by extracting square roots - x2=24x^{2}=24x2=24