Math 2H Unit 6 Review Solving Quadratics

Review/Factoring

100

Use the Zero Product Property to solve the following quadratic equation. 2x(x - 7)(x + 2) = 0

x = 7, x = -2, x = 0

200

Solve the following quadratic equation by factoring. 2x² + 6x + 4 = 0

x = -2 x = -1

300

Factor

4x² - 81y²

(2x + 9y)(2x - 9y)

400

Solve the following quadratic equation by factoring. 2x² + 17x = -21

x = -7 x = -3/2

500

Solve the following quadratic equation by factoring. 5x² = x + 18

x = -9/5 x = 2

Square Roots

100

Solve the following quadratic equation by using square roots: x² = 4

x = 2 x = -2

200

Solve the following quadratic equation by using square roots: x² - 121 = 0

+11 or -11

300

Solve the following quadratic equation by using square roots: 4x² - 100 = 300

x = 10 x = -10

400

Solve the following quadratic equation by using square roots: 2(x+5)² -10 = 40

x = 0 x = -10

500

Solve the following quadratic equation by using square roots: 5(x+2)² = -40

x = -2 + 2i√2 x = -2 - 2i√2

Completing the Square

100

Solve the following quadratic equation by completing the square: x² + 6x = -8

x = -2 x = -4

200

Solve the following quadratic equation by completing the square: x² - 6x = -6

x = 3 +-√3

300

Solve the following quadratic equation by completing the square: x² - 2x - 24 = 0

x = -4 x = 6

400

Solve the following quadratic equation by completing the square: 2x² + 20x - 30 = 0

x = -5 +-2√10

Quadratic Formula

100

What is the discriminant of 3x² - 2x - 8 = 0?

100

200

If the discriminant is "0", how many solutions are there?

What is 1 solution? (A positive is 2 solutions and a negative is 0 solutions)

300

Solve the following quadratic equation by using the quadratic formula: 2x² - x - 4 = 2

x = 2 x = -3/2

400

Solve the following quadratic equation by using the quadratic formula: x² - 5x - 5 = 0

x = (5+3√ 5)/2,   x = (5- 3√ 5)/2

500

Solve the following quadratic equation by using the quadratic formula: 4x² - 17x - 15 = 0

x = 5 x = -3/4

Models & i

100

Multiply (3 + 7i)(4i - 8)

-52 - 44i

200

Solve

x^2+4x=-5

-2+-i

300

The function h = -16t² + h₀ gives the height (in feet) of a ball dropped from a height of "h₀" after "t" seconds. A ball is dropped from a height of 64 feet. After how many seconds does the ball hit the floor (h=0)?

2 seconds

400

Jimbo is throwing a water ballon from the top of his 10 ft. shack.  He throws it up at a velocity of 42 ft/s.  When will it hit the ground? Round to the nearest tenth of a second.  h = -16t² + (v₀)t + h₀

2.8 seconds

500

The area of a platform is 28 ft². If the length is (x+2) and the width is (x+5) find the measure of each dimension.

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