Question 1

Simplify.$\sqrt{-16}$

Accepted Answer

$4i$

Answer

$-4$

Answer

$4$

Answer

$16i$

Question 2

Solve.    $3(x-4)^2+2=23$

Accepted Answer

$4\pm\sqrt{7}$

Answer

$4\pm\frac{\sqrt{21}}{3}$

Answer

$\sqrt{7}$

Answer

$4\sqrt{7}$

Question 3

Simplify. $\sqrt{128}$

Accepted Answer

$8\sqrt{2}$

Answer

$4\sqrt{8}$

Answer

$2\sqrt{32}$

Answer

$4\sqrt{32}$

Question 4

Solve. $x^2-5x-24=0$

Accepted Answer

$x=8$ and $x=-3$

Answer

$\frac{5 \pm \sqrt{121}}{3}$

Answer

8

Answer

$\frac{5 \pm i\sqrt{71}}{3}$

Question 5

Which of the following quadratic equations has no real solutions?

Accepted Answer

$2x^2-4x+3=0$

Answer

$x^2-6x-2=0$

Answer

$x^2+3x-5=0$

Answer

$4x^2+4x+1=0$

Question 6

Solve. $2x^2-12=69$

Accepted Answer

$\pm \frac{9 \sqrt{2}}{2}$

Answer

$\pm \frac{\sqrt{57} }{\sqrt2}$

Answer

$\pm \frac{9}{2}$

Answer

$\pm \frac{9 }{\sqrt2}$

Question 7

Which equation shows $x^2+4x-10=0$ after the method of completing the square has been applied?

Accepted Answer

$(x+2)^2=14$

Answer

$(x+2)^2=10$

Answer

$(x+4)^2=10$

Answer

$(x+4)^2=6$

Question 8

Simplify. $\sqrt{-162}$

Accepted Answer

$9i\sqrt{2}$

Answer

$18i$

Answer

$-9\sqrt{2}$

Answer

$2i\sqrt{81}$

Question 9

Add. $(8+4i)+(2-6i)$

Accepted Answer

$10-2i$

Answer

$10+2i$

Answer

$10+10i$

Answer

$10-10i$

Question 10

Recall for falling objects:
 $h(t)=h_0-16t^2$ where $h$ is the height of the object, in feet, at any time $t$, in seconds, and $h_0$ is the object’s initial height in feet.  A carpenter dropped a hammer from a rooftop 48 feet above ground.  How long, in seconds, did it take the hammer to hit the ground? (round to the nearest tenth)

Accepted Answer

1.7

Answer

16

Answer

76

Answer

3

Question 11

Subtract. $(6+2i)-(8-9i)$

Accepted Answer

$-2+11i$

Question 12

Solve.    $4x^2-1=-8x$

Accepted Answer

$\frac{-2\pm\sqrt5}{2}$

Answer

$\frac{-1\pm\sqrt5}{2}$

Answer

$\frac{1\pm\sqrt5}{2}$

Answer

$\frac{2\pm\sqrt5}{2}$

Question 13

$(3+2i)(1-4i)$

Accepted Answer

$11-10i$

Answer

$-5-10i$

Answer

$3+10i-8i^2$

Answer

$11+10i$

Question 14

Simplify $i^{38}$

Accepted Answer

$-1$

Answer

$i$

Answer

$-i$

Answer

$1$

Question 15

Find the discriminant of the equation.  Then determine the number of the real or nonreal solutions.  $x^2-3x+8$

Accepted Answer

2 imaginary or complex solutions

Answer

1 imaginary or complex solution

Answer

2 real solutions

Answer

1 real solution

Question 16

Solve. $-3x^2+18x=-30$

Accepted Answer

$3\pm \sqrt{19}$

Answer

$\frac{3\pm \sqrt{19}}{3}$

Answer

$3\pm \sqrt{51}$

Answer

$\frac{-9\pm \sqrt{51}}{3}$

Question 17

Find the equation of a parabola with a focus of (2,5) and a directrix of x=-4.

Accepted Answer

$(y-5)^2=12(x+1)$

Answer

$(y-5)^2=3(x-5)$

Answer

$(y-5)^2=12(x-5)$

Answer

$(y-5)^2=3(x+1)$

Question 18

Find the equation of a parabola with a focus of (1,8) and a vertex of (1,-2).

Accepted Answer

$(x-1)^2=40(y+2)$

Answer

$(x-2)^2=40(y+1)$

Answer

$(x+2)^2=40(y-1)$

Answer

$(x+1)^2=40(y-2)$

Question 19

Find the equation of a parabola with a vertex of (4,2) and a directrix of x=8.

Accepted Answer

$(y-2)^2=-16(x-4)$

Answer

$(y-4)^2=-4(x-2)$

Answer

$(y-2)^2=16(x-4)$

Answer

$(y-4)^2=-16(x-2)$

Question 20

An equation for a cross section of a flashlight’s parabolic reflector can be modeled by $y^2=36x$ . The light bulb is at the focus of the parabolic reflector. What is the focus?

Accepted Answer

$(9,0 )$

Answer

$(0,0 )$

Answer

$(0,9 )$

Answer

$(9,9 )$

Question 21

Write an equation in standard form for the parabola whose graph is shown.

Accepted Answer

$(y-2)^2=20(x+3)$

Answer

$(x-2)^2=20(y+3)$

Answer

$(y-3)^2=20(x+2)$

Answer

$(x+3)^2=20(y-2)$

Question 22

A microphone is placed at the focus of a parabolic reflector to collect sounds for the television broadcast of a football game.  The microphone is 6 inches away from the center of the reflector.  The width of the reflector is 36 inches across.  How deep is the reflector?

Accepted Answer

13.5 inches

Answer

24 inches

Answer

18 inches

Answer

6 inches

Question 23

An engineer designs a satellite dish with a parabolic cross-section.  The dish is 15 ft. wide at the opening and the depth is 4 feet.  Find the position of the light source (the focus).

Accepted Answer

3.5 ft

Answer

8 ft

Answer

7.5 ft

Answer

4 ft

Question 24

Solve. $x^2+2x-24\leq0$

Accepted Answer

$\{{x\mid -6\leq x \leq4}\}$

Answer

$\{{x\mid x\leq-6\ or\ x \geq4}\}$

Answer

$\{{x\mid -4\leq x \leq4}\}$

Answer

$\{{x\mid x\leq4\ or\ x \geq4}\}$

Question 25

Solve  $2x^2+5x\leq12$

Accepted Answer

$\{{x\mid -6\leq x \leq1}\}$

Answer

$\{{x\mid x\leq -4 \ or\ x \geq2}\}$

Answer

$\{{x\mid -4\leq x \leq2}\}$

Answer

$\{{x\mid x\leq -6 \ or\ x \geq1}\}$

Related quizzes

Related quizzes