Solving Quadratic Equations

Factoring

100

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

x = 7 x = -2

200

Solve the following quadratic equation by factoring. x²+3x+2 = 0

x = -2 x = -1

300

Solve the following quadratic equation by factoring. x² - 6x + 5 = 0

x = 5 x = 1

400

Solve the following quadratic equation by factoring. 9x² - 64  = 0

x = 8/3  x = -8/3

500

Solve the following quadratic equation by factoring. 2x² - 5x - 3 = 0

x = -1/2 x = 3

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

+11 or -11

300

Solve the following quadratic equation by using square roots: 4x² = 400

x = 10 x = -10

400

Solve the following quadratic equation by using square roots: x² -9 = -8

1 or -1

500

Solve the following quadratic equation by using square roots: 5x² + 3 = 128

x = 5 x = -5

Imaginary/Complex Answers

100

Solve the following quadratic equation and state the answer in simplest radical form: x² + 4 = 0

x = +- 2i

200

Solve the following quadratic equation:  x² +20 = 0

x =+-2i sqrt(5)

300

Solve the following quadratic equation and write the answer in simplest radical form: 2x² - 6x - 3 = 0

x=(3+- sr(15))/2

400

Solve the following quadratic equation and state the answer in simplest radical form: x² + 3x + 10 =0

x = (-3 +- isqrt(31))/2

500

Solve the following quadratic equation and write the answer in simplest radical form: 4x² + 11x = 3x - 10

x = -2 +- i sr(6) / 2

Word Problems and grouping

100

Find two consecutive odd integers whose product is 143

x = 11

x = 13

200

Solve the following by factoring by grouping: 

x³ + 6x² + 5x+30 = 0

x = -6

x = +- isqr5

300

Solve the following quadratic equation by using the quadratic formula: x² - 9x + 20 = 0

x = 5 x = 4

400

Solve the following: 2x³ + 9x² + 4x+18 = 0

x = -1/2 x = -4

500

A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 ft/s.

The height of the rocket at any time t is given by:

h(t) = -16t² +116t + 101

At what time does the rocket hit the ground?  Round to the nearest whole number.

t = 8 seconds

Miscellaneous

100

Name 2 of the three other words that are synonymous with "solution"

root, zeroes, x-intercepts

200

What is the quadratic formula?

x = -b +- sqrt(b² - 4ac) /(2a)

300

Find the discriminant of  f(x)=5x²+2x-2 and state how many and what kind of answer you should expect

44

2 real (irrational) answers

400

f(x)=-x²-4x

(-2,4)

500

Find the vertex of x=5y²+4y+3

(11/5,-2/5)