Solving Real Number Quadratics

A soccer ball is kicked from the ground with an initial upward velocity of 90 feet per second. The equation h=-16t² + 90t gives the height h of the ball after t seconds.
How many seconds will it take the ball to hit the ground?

• 126.56 ft

• 5.625 sec

• 2.81 sec

• 0 ft

How many solutions does the equation 4x² + 4x + 1 = 0 have?

• 0

• 1

• 2

• More than 2

Solve using the Quadratic Formula

6x² + 12x - 1 = 0

• x = 0.08, -2.08

• x = -0.08, 2.08

• x = -0.08, -1.91

• x = 0.08, 1.19

Solve using the Quadratic Formula

6x² - 52 = 11x

• x = 4, -2.17

• x = -4, 2.17

• x = -3.71, -1.88

• x = 3.71, 1.88

Solve
 3x² + 5x - 12 = 0

• x = -4/3, x = 3

• x = 4/3, x = -3

• x = -1, x = 4

• x = 1, x = -4

Solve by factoring:  4x² + 11x - 3 = 0

• x = -3/4 and x = -1

• x = 4 and x = 3

• x = 1/4 and x = -3

• x = -1/4 and x = 3

What is the discriminant?

• b²-4ac

• b²/2a

• 4ac

• b²±4ac

If the discriminant is zero you will have

• no real solutions

• two real solutions

• 1 real solution

• 1 imaginary solution

Use the graph to determine the solutions.

• -1 and -3

• 1 and -3

• 1 and 3

• -1 and 3

How many solutions does this graph have?

• one

• two

• no solutions

• cannot be determined