Question 1

Solve the equation by using the quadratic formula. $$3 x ^ { 2 } + 9 x - 12 = 0$$

Accepted Answer

{1, -4}

Question 2

Solve the rational inequality. Write the answer in interval notation. $$\frac { 3 x - 7 } { 13 + 2 x } < 0$$

Accepted Answer

A)  $\left( - \infty , - \frac { 13 } { 2 } \right) \cup \left( \frac { 7 } { 3 } , \frac { 13 } { 2 } \right)$ 
B)  $\left( - \frac { 13 } { 2 } , \frac { 7 } { 3 } \right)$ 
C)  $\left( - \frac { 7 } { 3 } , \frac { 13 } { 2 } \right)$ 
D)  $\left( - \infty , - \frac { 7 } { 3 } \right) \cup \left( \frac { 13 } { 2 } , \infty \right)$ 
A)  $\left( - \infty , - \frac { 13 } { 2 } \right) \cup \left( \frac { 7 } { 3 } , \frac { 13 } { 2 } \right)$ 
B)  $\left( - \frac { 13 } { 2 } , \frac { 7 } { 3 } \right)$ 
C)  $\left( - \frac { 7 } { 3 } , \frac { 13 } { 2 } \right)$ 
D)  $\left( - \infty , - \frac { 7 } { 3 } \right) \cup \left( \frac { 13 } { 2 } , \infty \right)$ B

Question 3

Find the vertex by using the vertex formula. $$h ( x ) = - 2 x ^ { 2 } + 16 x - 3$$

Accepted Answer

A)  $( 16 , - 3 )$ 
B)  $( 0 , - 3 )$ 
C)  $( 4,29 )$ 
D)  $( - 2,13 )$ 
A)  $( 16 , - 3 )$ 
B)  $( 0 , - 3 )$ 
C)  $( 4,29 )$ 
D)  $( - 2,13 )$ C

Question 4

Solve the quadratic equation by completing the square and applying the square root property. $$( 3 w + 2 ) ( w - 1 ) = 5$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 6 } - \frac { \sqrt { 83 } } { 6 } , \frac { 1 } { 6 } + \frac { \sqrt { \sqrt { 83 } } } { 6 } \right\}$ 
B)  $\left\{ \frac { 1 } { 6 } - \frac { i \sqrt { 83 } } { 6 } , \frac { 1 } { 6 } + \frac { i \sqrt { \sqrt { 83 } } } { 6 } \right\}$ 
C)  $\left\{ \frac { 1 } { 6 } - \frac { \sqrt { 85 } } { 6 } , \frac { 1 } { 6 } + \frac { \sqrt { 85 } } { 6 } \right\}$ 
D)  $\left\{ - \frac { 2 } { 3 } , 1 \right\}$ 
A)  $\left\{ \frac { 1 } { 6 } - \frac { \sqrt { 83 } } { 6 } , \frac { 1 } { 6 } + \frac { \sqrt { \sqrt { 83 } } } { 6 } \right\}$ 
B)  $\left\{ \frac { 1 } { 6 } - \frac { i \sqrt { 83 } } { 6 } , \frac { 1 } { 6 } + \frac { i \sqrt { \sqrt { 83 } } } { 6 } \right\}$ 
C)  $\left\{ \frac { 1 } { 6 } - \frac { \sqrt { 85 } } { 6 } , \frac { 1 } { 6 } + \frac { \sqrt { 85 } } { 6 } \right\}$ 
D)  $\left\{ - \frac { 2 } { 3 } , 1 \right\}$

Question 5

The hypotenuse of a right triangle is 7 ft long. One leg is 1.4 ft longer than the other leg. Find the lengths of the legs. Round to 1 decimal place.

Accepted Answer

A)  1.4 ft2 and 5.6 ft2 
B)  1.4 ft and 5.6 ft 
C)  4.1 ft2 and 5.7 ft2 
D)  4.2 ft and 5.6 ft 
A)  1.4 ft2 and 5.6 ft2 
B)  1.4 ft and 5.6 ft 
C)  4.1 ft2 and 5.7 ft2 
D)  4.2 ft and 5.6 ft

Question 6

The daily profit in dollars made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. Find the maximum possible daily profit.

Accepted Answer

A)  $8,075 
B)  $9,448 
C)  $10,125 
D)  $15,275 
A)  $8,075 
B)  $9,448 
C)  $10,125 
D)  $15,275

Question 7

a. Factor the expression $x ^ { 3 } - 27$ 
b. Use the zero product rule and the quadratic formula to solve the equation $x ^ { 3 } - 27 = 0$ = 0. There should be three solutions.

Accepted Answer

A)  a. $( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)$
b. $\left\{ 3 , \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}$ 
B)  a. $( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)$
b. $\left\{ 3 , - \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}$ 
C)  a. $( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)$
b. $\left\{ 3 , \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}$ 
D)  a. $( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)$
b. $\left\{ 3 , - \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}$ 
A)  a. $( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)$
b. $\left\{ 3 , \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}$ 
B)  a. $( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)$
b. $\left\{ 3 , - \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}$ 
C)  a. $( x + 3 ) \left( x ^ { 2 } - 3 x + 9 \right)$
b. $\left\{ 3 , \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}$ 
D)  a. $( x - 3 ) \left( x ^ { 2 } + 3 x + 9 \right)$
b. $\left\{ 3 , - \frac { 3 } { 2 } \pm \frac { 3 \sqrt { 3 } } { 2 } i \right\}$

Question 8

Solve the equation by using the square root property. $$t ^ { 2 } = - 49$$

Accepted Answer

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

Question 9

Find the value of k so that the expression is a perfect square trinomial and then factor the trinomial. $$y ^ { 2 } - 8 y + k$$

Accepted Answer

A)  $k = 16 ; ( y - 4 )$ 
B)  $k = 4 ; ( y - 4 ) ^ { 2 }$ 
C)  $k = 4 ; ( y + 4 ) ^ { 2 }$ 
D)  $k = 16 ; ( y - 4 ) ^ { 2 }$ 
A)  $k = 16 ; ( y - 4 )$ 
B)  $k = 4 ; ( y - 4 ) ^ { 2 }$ 
C)  $k = 4 ; ( y + 4 ) ^ { 2 }$ 
D)  $k = 16 ; ( y - 4 ) ^ { 2 }$

Question 10

Find the vertex by using the vertex formula. $$f ( x ) = x ^ { 2 } + 10 x - 6$$

Accepted Answer

A)  $\left( - 5 , \frac { 11 } { 4 } \right)$ 
B)  $( 10 , - 6 )$ 
C)  $( - 5 , - 31 )$ 
D)  $( - 10,6 )$ 
A)  $\left( - 5 , \frac { 11 } { 4 } \right)$ 
B)  $( 10 , - 6 )$ 
C)  $( - 5 , - 31 )$ 
D)  $( - 10,6 )$

Question 11

Use the standard form of a parabola given by $y = a x ^ { 2 } + b x + c$ to write an equation of a parabola that passes through the points $( 4,4 ) , ( 1,13 )$ and $( 3,1 )$.

Accepted Answer

A)  $y = 3 x ^ { 2 } - 24 x + 49$ 
B)  $y = 3 x ^ { 2 } - 12 x + 13$ 
C)  $y = 3 x ^ { 2 } - 18 x + 28$ 
D)  $y = 3 x ^ { 2 } - 12 x - 13$ 
A)  $y = 3 x ^ { 2 } - 24 x + 49$ 
B)  $y = 3 x ^ { 2 } - 12 x + 13$ 
C)  $y = 3 x ^ { 2 } - 18 x + 28$ 
D)  $y = 3 x ^ { 2 } - 12 x - 13$

Question 12

Solve the equation by using the square root property. $$( 2 z - 4 ) ^ { 2 } + 12 = 4$$

Accepted Answer

A)  $\{ 2 \sqrt { 2 } - 4 \}$ 
B)  $\{ 2 \sqrt { 2 } + 4 \}$ 
C)  $\{ 2 + i \sqrt { 2 } , 2 - i \sqrt { 2 } \}$ 
D)  $\{ 4 + 2 \sqrt { 2 } , - 4 + 2 \sqrt { 2 } \}$ 
A)  $\{ 2 \sqrt { 2 } - 4 \}$ 
B)  $\{ 2 \sqrt { 2 } + 4 \}$ 
C)  $\{ 2 + i \sqrt { 2 } , 2 - i \sqrt { 2 } \}$ 
D)  $\{ 4 + 2 \sqrt { 2 } , - 4 + 2 \sqrt { 2 } \}$

Question 13

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. $$t ^ { 2 } - \frac { 2 } { 3 } t + n$$

Accepted Answer

The answer of Find the value of n so that...

Question 14

a. Find the vertex.
b. Find the y-intercept.
c. Find the x-intercept(s), if they exist.
d. Use this information to graph the function. $$h ( x ) = - \frac { 1 } { 4 } x ^ { 2 } + \frac { 2 } { 3 }$$

Accepted Answer

a. @#LAT-DLM&
b. @#LAT-DLM&
c.

Question 15

Find the x- and y-intercepts of the function. $$g ( x ) = x ^ { 2 } + 3 x + 8$$

Accepted Answer

x-intercep

Question 16

Use the discriminant to determine the type and number of solutions. $3 x ^ { 2 } + 3 x + 2 = 0$

Accepted Answer

A)  Two imaginary solutions 
B)  Two irrational solutions 
C)  Two rational solutions 
D)  One rational solution 
A)  Two imaginary solutions 
B)  Two irrational solutions 
C)  Two rational solutions 
D)  One rational solution

Question 17

A 10 foot ladder is leaning against a vertical wall so that the distance from its base to the wall is 1 foot less than the distance from its top to the floor. How far away from the wall is the base of the ladder? Round to the nearest hundredth of a foot.

Accepted Answer

The answer of A 10 foot ladder is leaning against...

Question 18

The temperature at a state park for one day in June can be approximated by the function $T ( x ) = 0.284 x ^ { 2 } - 5.11 x + 82 \quad 0 \leq x \leq 18$ where T is degrees Fahrenheit and x is the number of hours after 5 PM on Friday. What was the lowest temperature reached? Round to the nearest whole degree.

Accepted Answer

A)  64 degrees 
B)  70 degrees 
C)  62 degrees 
D)  59 degrees 
A)  64 degrees 
B)  70 degrees 
C)  62 degrees 
D)  59 degrees

Question 19

Write the function in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ by completing the square.
$$g ( x ) = - 3 x ^ { 2 } + 15 x + 2$$

Accepted Answer

A)  $g ( x ) = - 3 \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 217 } { 12 }$ 
B)  $g ( x ) = - 3 ( x + 15 ) ^ { 2 } + 2$ 
C)  $g ( x ) = - 3 \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 83 } { 4 }$ 
D)  $g ( x ) = - 3 ( x + 5 ) ^ { 2 } - \frac { 2 } { 3 }$ 
A)  $g ( x ) = - 3 \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 217 } { 12 }$ 
B)  $g ( x ) = - 3 ( x + 15 ) ^ { 2 } + 2$ 
C)  $g ( x ) = - 3 \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 83 } { 4 }$ 
D)  $g ( x ) = - 3 ( x + 5 ) ^ { 2 } - \frac { 2 } { 3 }$

Question 20

Graph the function. $$g ( x ) = ( x + 6 ) ^ { 2 }$$

Accepted Answer

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

Solve the equation by using the quadratic formula. $3 x ^ { 2 } + 9 x - 12 = 0$

Solve the rational inequality. Write the answer in interval notation. $\frac { 3 x - 7 } { 13 + 2 x } < 0$

Find the vertex by using the vertex formula. $h ( x ) = - 2 x ^ { 2 } + 16 x - 3$

Solve the quadratic equation by completing the square and applying the square root property. $( 3 w + 2 ) ( w - 1 ) = 5$

The hypotenuse of a right triangle is 7 ft long. One leg is 1.4 ft longer than the other leg. Find the lengths of the legs. Round to 1 decimal place.

The daily profit in dollars made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. Find the maximum possible daily profit.

a. Factor the expression $x ^ { 3 } - 27$ b. Use the zero product rule and the quadratic formula to solve the equation $x ^ { 3 } - 27 = 0$ = 0. There should be three solutions.

Solve the equation by using the square root property. $t ^ { 2 } = - 49$

Find the value of k so that the expression is a perfect square trinomial and then factor the trinomial. $y ^ { 2 } - 8 y + k$

Find the vertex by using the vertex formula. $f ( x ) = x ^ { 2 } + 10 x - 6$

Use the standard form of a parabola given by $y = a x ^ { 2 } + b x + c$ to write an equation of a parabola that passes through the points $( 4,4 ) , ( 1,13 )$ and $( 3,1 )$ .

Solve the equation by using the square root property. $( 2 z - 4 ) ^ { 2 } + 12 = 4$

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. $t ^ { 2 } - \frac { 2 } { 3 } t + n$

a. Find the vertex. b. Find the y-intercept. c. Find the x-intercept(s), if they exist. d. Use this information to graph the function. $h ( x ) = - \frac { 1 } { 4 } x ^ { 2 } + \frac { 2 } { 3 }$

Find the x- and y-intercepts of the function. $g ( x ) = x ^ { 2 } + 3 x + 8$

Use the discriminant to determine the type and number of solutions. $3 x ^ { 2 } + 3 x + 2 = 0$

A 10 foot ladder is leaning against a vertical wall so that the distance from its base to the wall is 1 foot less than the distance from its top to the floor. How far away from the wall is the base of the ladder? Round to the nearest hundredth of a foot.

Write the function in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ by completing the square. $g ( x ) = - 3 x ^ { 2 } + 15 x + 2$

Graph the function. $g ( x ) = ( x + 6 ) ^ { 2 }$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

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Exam 7: Quadratic Equations, Functions and Inequalities

Solve the equation by using the quadratic formula. 3x2+9x−12=03 x ^ { 2 } + 9 x - 12 = 03x2+9x−12=0

Solve the rational inequality. Write the answer in interval notation. 3x−713+2x<0\frac { 3 x - 7 } { 13 + 2 x } < 013+2x3x−7​<0

Find the vertex by using the vertex formula. h(x)=−2x2+16x−3h ( x ) = - 2 x ^ { 2 } + 16 x - 3h(x)=−2x2+16x−3

Solve the quadratic equation by completing the square and applying the square root property. (3w+2)(w−1)=5( 3 w + 2 ) ( w - 1 ) = 5(3w+2)(w−1)=5

The hypotenuse of a right triangle is 7 ft long. One leg is 1.4 ft longer than the other leg. Find the lengths of the legs. Round to 1 decimal place.

The daily profit in dollars made by an automobile manufacturer is P(x)=−45x2+2,250x−18,000P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000P(x)=−45x2+2,250x−18,000 where x is the number of cars produced per shift. Find the maximum possible daily profit.

a. Factor the expression x3−27x ^ { 3 } - 27x3−27 b. Use the zero product rule and the quadratic formula to solve the equation x3−27=0x ^ { 3 } - 27 = 0x3−27=0 = 0. There should be three solutions.

Solve the equation by using the square root property. t2=−49t ^ { 2 } = - 49t2=−49

Find the value of k so that the expression is a perfect square trinomial and then factor the trinomial. y2−8y+ky ^ { 2 } - 8 y + ky2−8y+k

Find the vertex by using the vertex formula. f(x)=x2+10x−6f ( x ) = x ^ { 2 } + 10 x - 6f(x)=x2+10x−6

Use the standard form of a parabola given by y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c to write an equation of a parabola that passes through the points (4,4),(1,13)( 4,4 ) , ( 1,13 )(4,4),(1,13) and (3,1)( 3,1 )(3,1) .

Solve the equation by using the square root property. (2z−4)2+12=4( 2 z - 4 ) ^ { 2 } + 12 = 4(2z−4)2+12=4

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. t2−23t+nt ^ { 2 } - \frac { 2 } { 3 } t + nt2−32​t+n

a. Find the vertex. b. Find the y-intercept. c. Find the x-intercept(s), if they exist. d. Use this information to graph the function. h(x)=−14x2+23h ( x ) = - \frac { 1 } { 4 } x ^ { 2 } + \frac { 2 } { 3 }h(x)=−41​x2+32​

Find the x- and y-intercepts of the function. g(x)=x2+3x+8g ( x ) = x ^ { 2 } + 3 x + 8g(x)=x2+3x+8

Use the discriminant to determine the type and number of solutions. 3x2+3x+2=03 x ^ { 2 } + 3 x + 2 = 03x2+3x+2=0

A 10 foot ladder is leaning against a vertical wall so that the distance from its base to the wall is 1 foot less than the distance from its top to the floor. How far away from the wall is the base of the ladder? Round to the nearest hundredth of a foot.

Write the function in the form f(x)=a(x−h)2+kf ( x ) = a ( x - h ) ^ { 2 } + kf(x)=a(x−h)2+k by completing the square. g(x)=−3x2+15x+2g ( x ) = - 3 x ^ { 2 } + 15 x + 2g(x)=−3x2+15x+2

Graph the function. g(x)=(x+6)2g ( x ) = ( x + 6 ) ^ { 2 }g(x)=(x+6)2

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Polynomials

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Solve the equation by using the quadratic formula. $3 x ^ { 2 } + 9 x - 12 = 0$

Solve the rational inequality. Write the answer in interval notation. $\frac { 3 x - 7 } { 13 + 2 x } < 0$

Find the vertex by using the vertex formula. $h ( x ) = - 2 x ^ { 2 } + 16 x - 3$

Solve the quadratic equation by completing the square and applying the square root property. $( 3 w + 2 ) ( w - 1 ) = 5$

The daily profit in dollars made by an automobile manufacturer is $P ( x ) = - 45 x ^ { 2 } + 2,250 x - 18,000$ where x is the number of cars produced per shift. Find the maximum possible daily profit.

a. Factor the expression $x ^ { 3 } - 27$ b. Use the zero product rule and the quadratic formula to solve the equation $x ^ { 3 } - 27 = 0$ = 0. There should be three solutions.

Solve the equation by using the square root property. $t ^ { 2 } = - 49$

Find the value of k so that the expression is a perfect square trinomial and then factor the trinomial. $y ^ { 2 } - 8 y + k$

Find the vertex by using the vertex formula. $f ( x ) = x ^ { 2 } + 10 x - 6$

Use the standard form of a parabola given by $y = a x ^ { 2 } + b x + c$ to write an equation of a parabola that passes through the points $( 4,4 ) , ( 1,13 )$ and $( 3,1 )$ .

Solve the equation by using the square root property. $( 2 z - 4 ) ^ { 2 } + 12 = 4$

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. $t ^ { 2 } - \frac { 2 } { 3 } t + n$

a. Find the vertex. b. Find the y-intercept. c. Find the x-intercept(s), if they exist. d. Use this information to graph the function. $h ( x ) = - \frac { 1 } { 4 } x ^ { 2 } + \frac { 2 } { 3 }$

Find the x- and y-intercepts of the function. $g ( x ) = x ^ { 2 } + 3 x + 8$

Use the discriminant to determine the type and number of solutions. $3 x ^ { 2 } + 3 x + 2 = 0$

Write the function in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ by completing the square. $g ( x ) = - 3 x ^ { 2 } + 15 x + 2$

Graph the function. $g ( x ) = ( x + 6 ) ^ { 2 }$