Quadratic Formula & the Discriminant

Quadratic Formula & the Discriminant

Today we will be practicing the Quadratic formula!

Let's do a couple practice problems

Multiple Choice

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

• a = 4, b = -8, c = 3

• a = 4, b =-8, c =-3

• a = 4, b = 8, c = 3

• a = 4, b = 8, c = -3

Multiple Choice

What is this formula?

• This is the standard formula.

• This is the quadratic formula.

• This is the square root formula.

• This is the Pythagorean formula

Multiple Choice

Solve Using the Quadratic Formula

x² + 4x - 40 = -8

• -10 & -4

• -4 & 10

• -8 & 4

• 8 & -4

Multiple Choice

Solve 2x² + 7x - 15 = 0

• -3/2 or 5

• No Solution

• -5 or 3/2

• 0.7 or 5

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

Awesome job! Sometimes with Quadratic Formula you will have to do word problems( I would write this on our page 63 and at least 1 word problem).

• They usually deal with time. When dealing with QF we usually have a positive and negative x intercepts. When dealing with problems with time, we can't have negative time so we would only use the positive intercept.

Multiple Choice

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

Multiple Choice

Solve the word problem:  How fast would you reach the water if you jump of a cliff using the formula:    h(t) = -16t² + 8t + 24?

• 8
• 1
• 1.5
• 1/4

Multiple Choice

The height of a water balloon that is launched into the air is given by h(t) = -5x²+20x+25. When will the balloon explode on the ground?

• 5 seconds

• 1 second

• 2 seconds

• 3 seconds

WRITE IN NOTEBOOK

We also have something called the discriminant. The discriminant is used ONLY to tell how many solutions a problem will have. The discriminant formula is b²-4ac (look familiar?)

• When the discriminant is >0 that means a problem has 2 solutions.

• When the discriminant is =0 that means the problem has 1 solution.

• When the discriminant is <0 that means the problem has no solutions.

Multiple Choice

What is the formula for the discriminant?

• x = -b/2a

• b² - 4ac

• a² + b² = c²

• x = [-b±√(b²-4ac)]/2a

Multiple Choice

If the discriminant is equal to 4, how many solutions are there?

• No Solutions

• 1 Solution

• 2 Solutions

• Infinite Solutions

Multiple Choice

What is the discriminant of this equation?

3x² + 8x = 0

• 64

• 52

• 9

• 0

Multiple Choice

What is the discriminant and how many solutions would this quadratic have?

4x² + 6x - 4 = 0

• -28, No Solutions

• 28, 2 Solutions

• 100, 2 Solutions

• -100, No Solutions

Multiple Choice

What is the discriminant and how many solutions would this quadratic have?

x² - 6x + 9 = 0

• 0, No Solutions

• 0, 1 Solution

• 72, 2 Solutions

• -72, No Solution

Multiple Choice

If the discriminant is equal to -2, how many solutions are there?

• No Solutions

• 1 Solution

• 2 Solutions

• Infinite Solutions

Multiple Choice

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

• No solutions

• 1 Solution

• 2 Solutions

• Infinite solutions