Module 18 Quadratics Review

Solve with Square Roots

100

x² = 144

x = 12, x = -12

200

5x² - 250 = 0

x = 7.07, -7.07 

300

10(x+4)² = 40

x=-6, x=-2

400

x² = ⁷/₄ 

*write your answer as a simplified radical

x=^sqrt7/₂ , x = -^{sqrt 7}/₂

500

-2(2x-3)²-6=0

*write your answer as a simplified radical

no solution

Complete the Square

100

What value of c will complete the square?

x² + 18x + c

c = 81

200

What value of c will complete the square?

¹/₂₅x² + ¹⁸/₅x + c

c = 81/25

300

Complete the square:  25x² - 20x + ___

What is the factored form of this expression?

(5x-2)²

400

Solve by completing the square:

16x² - 8x = 8

x=1, x=-¹/₂

500

Solve by completing the square. Write your answer as a simplified radical.

4x²-32x=-27

x=4 + ^sqrt37/₂ , x= 4 - ^sqrt37/₂ 

Solve by Factoring

100

x² - 16x - 36=0

x=-2, x=18

200

x² - 15x = -54

x=6, x=9

300

2x²+ 7x - 30=0

x=-6, x=2.5

400

3x² - 8 = 10x

x = -²/₃ , x = 4

500

-1.5x² - 4.5x = -15

x=2, x=-5

Quadratic Formula

100

-x² - 5x + 24 = 0

x = 3, x = -8

200

2x² - 16x = -30

x = 3, x = 5

300

7.5x² - 15x = 60

x = -2, x = 4

400

114x² - 205x + 84 = 0

*write your answers as simplified fractions

x = ⁷/₆ , x = ¹²/₁₉

500

7x² - 8x = 13

*write your answer as a simplified radical

x = ^{4 + sqrt107}/₇ , x = ^{4 - sqrt 107}/₇

Random Quadratics Questions

100

What is the discriminant of the equation:

4x² +6x=-32?

-476

200

What is the vertex of the parabola:

f(x) =-3x² - 18x - 23.

(-3, 4)

300

Tell how many solutions each equation has

A)     x(x + 18) = -1

B)     x + 25 =-x²

C)      x²+ 14x + 49 = 0

A) two solutions

B) no solution

C) one solution

400

A cylindrical glass vase has a volume of 483π cubic centimeters and measures 21 centimeters tall.

What is the exact diameter of the base of the vase in centimeters?

diameter = 2*sqrt23 cm 

500

What is the discriminant of the equation:

2x(5x -6) = -x² - 1

100