Solving Quadratics Quiz Review

Fantastic Factoring

100

Solve by factoring

x² - 8x - 20 = 0

(x-10)(x+2)=0

x=10,-2

200

Solve by factoring.

3x² - 12x=0

3x(x-4)=0

x = 0,4

300

Solve by factoring.

2x² + 5x = 3

2x²+5x-3=0

(2x-1)(x+3)=0

x=1/2, -3

400

Solve by factoring.

x³ = 36x

x³-36x=0

x(x²-36)=0

x(x+6)(x-6)=0

x = 0, 6, -6

500

Solve by factoring.

(3x + 7)(x - 3) = -16

3x²-9x+7x-21=-16

3x²-2x-5=0

(3x-5)(x+1)=0

x = 5/3,-1

Captivating CTS

100

Find the number that completes the square.

x² - 24x + ______

(-24/2)²

144

200

Find the number that completes the square.

x² + (1/2)x + ______

1/16

300

Solve by completing the square.

x² - 6x - 16 = 0

x²-6x=16

x²-6x+9=16+9

(x-3)²=25

x-3=±5

x=3±5

x = 8,-2

400

Solve by completing the square

x²- 4x - 1 =0

x²- 4x = 1

x²- 4x +4 =1+4

(x-2)²=5

x-2=±√5

x = 2 ± √5

500

Solve by completing the square.

5r² = 40r + 5

r² - 8r = 1

r² - 8r +16 = 1+16

(r-4)²=17

r-4=±√17

x = 4 ±√17

QuirkyQuadratic Formula (plus Discriminant)

100

Find the value of the discriminant and determine the number of real solutions.

2x²+5x-4=0

discriminant = b²-4ac

d = (5)²-4(2)(-4)

d = 57

2 real solutions

200

Find the value of the discriminant and determine the number of real solutions.

x² + 6x + 11 = 0

d = (6)²-4(1)(11)

d = -8

No real solutions

300

Solve by quadratic formula.

x² -4x+7=0

x = [4 ±√16-4(1)(7)] / 2(1)

x = [4 ±√16-28] / 2

x = [4 ±√-12] / 2

x = NO SOLUTION  (negative under square root)

400

Solve x² - 8x + 14 = 0 using the quadratic formula. 

x =[ 8 ± √64-4(1)(14) ] / 2(1)

x = [8 ± √8 ] / 2

x = [ 8 ± 2√2 ] / 2

x = 4 ± √2

500

Solve 2x² = 7x + 6 by using quadratic formula.

2x² - 7x - 6 = 0

x = [ 7  ±√49 - 4(2)(-6) ] / 2(2)

x  = (7 ±√ 97) / 4

Sigma Square Roots

100

What do you have to do first to solve quadratics equation by taking square roots?

Isolate the squared part

200

Solve this equation by taking square roots.

2x² + 1 = 73

2x² = 72

x² = 36

x= ±6

300

Solve this equation by taking square roots.

3x² - 10 = 62

3x²  = 72

x² =24

x = ±2√6

400

Solve this equation by taking square roots.

(x-4)² - 16 = 0

(x-4)² = 16

x- 4 =± 4

x = 4 ± 4 

x = 0 or 8

500

Solve this equation by taking square roots.

2(3x+2)² - 8 = 0

2(3x+2)²  =8

(3x+2)²  = 4

3x+2 = ± 2

3x = -2±2

x = (-2±2)/3

x = 0 , -4/3

Do you really know it?

100

What is the zero product property?

If ab = 0, then a = 0, or b = 0

200

Find the approximate solutions rounded to the tenth.

x = 5±√2

x = 6.4, 3.6

300

Write the quadratic formula from memory.

x = (-b± √b²-4ac)/2a

400

If the discriminant is a perfect square, the solutions will be _____________

rational

500

The quadratic formula is derived from standard form using which method?

Completing the square