Quadratic Formula & Discriminant Review

Quadratic Formula & Discriminant Review

You will need a calculator and a place to write your work.

The Quadratic Formula

• Put equation in standard form and set equal to zero (ex.  $ax^2+bx+c=0$ )

• Identify a, b, and c

• Substitute a,b, and c into equation 

• Simplify!

Multiple Choice

What is the quadratic formula?

• $x=-b\pm\sqrt{b^2-4ac}$

• $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

• $x=\frac{-b-\sqrt{b-4ac}}{2}$

• $x=-\frac{b}{2a}$

Multiple Choice

What part of a parabola does the quadratic formula help us find?

• Vertex

• Maximum

• Y-Intercept

• X-Intercept

Multiple Choice

Determine the values of

a, b, and c for

the quadratic equation:

0= x² +5x +7

• a=0, b=5, c=7

• a=1, b=5, c=7

• a=7, b=5, c=1

Multiple Choice

Determine the values of

a, b, and c for

the quadratic equation:

4x² – 8x = 3

*remember one side should =0

• 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

Use the quadratic formula to find the solutions for

0 = -x² - 5x + 12

• -4.9 and -0.1

• -8.54 and 8.54

• -0.45 and 3.55

• -6.77 and 1.77

Multiple Choice

Solve Using the Quadratic Formula

x² + 4x - 40 = -8

*remember one side should = 0

• -10 & -4

• -4 & 10

• -8 & 4

• 8 & -4

Multiple Choice

The discriminant is

• aX² + bX + c

• b - 4ac

• b² - 4ac

• b² + 4ac

Multiple Choice

____________

For the function above, is the discriminant positive, negative, or zero?

• Positive

• Negative

• Zero

• Cannot be determined

Multiple Choice

____________

For the function above, is the discriminant positive, negative, or zero?

• Positive

• Negative

• Zero

• Cannot be determined

Multiple Choice

For the function above, is the discriminant positive, negative, or zero?

• Positive

• Negative

• Zero

• Cannot be determined

How to Find the Discriminant

• Put the equation into standard form and set equal to zero

• Identify a, b, and c

• Substitute a, b, and c into  $b^2-4ac$  

• Simplify 

Multiple Choice

Determine the value of the discriminant and how many solutions the equation has.

x² + 7x + 13 = 0

• 400, 2 real solutions

• -3, 2 real solution

• -400, 0 real solutions

• -3, no real solutions

Multiple Choice

Find the discriminant of the following equation. (Hint: make =0 first!)

3x² -x + 3 = 5

• 5

• 25

• -24

• -26

Let's Mix it Up

For the next questions we will switch between finding the discriminant and using the quadratic formula. Let's see if you are up for the challenge!

Multiple Choice

 $-18x=x^2+81$  

Find the discriminant and number  of solutions

• -18 two solution

• 0, one solution

• -9, two solution

• 0, two solutions

• -9, two solutions

Multiple Choice

 $4x^2-4x-24=0$  

Find the discriminant and  number of solutions

• -4, two solutions

• 400, two solutions

• -4, two solutions

• 400, one solution

• 20, two solutions

Multiple Choice

Solve using the quadratic formula

x² - 14x = -49

• x = 1

• x = 2

• x = 7

• x = 21

Multiple Choice

Solve using quadratic formula

 $3x^2+6x+3=0$  

• x = -1

• x = 1,3

• x = 3

• x= - 1, - 3

Multiple Choice

Use the discriminant to determine the number of solutions

4x² + 4x + 1 = 0 has?

• 0

• 1

• 2

• More than 2

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?

-8x² + 6x - 4 = 0

• -92, No Solutions

• 164, 2 Solutions

• -164, No Solutions

• 92, 2 Solutions

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 4, 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

Multiple Choice

Use the discriminant to determine the number of solutions the following quadratic equation has.

-2x² − x − 1 = 0

• 76 Two Solutions

• -7 No Solutions

• 9 Two Solutions

• 0 One Solution

Multiple Choice

For the function below, is the discriminant positive, negative, or zero?

___________

y = x² + 4x + 4

• Positive

• Negative

• Zero

• Not Sure

Multiple Choice

Use the quadratic formula to find the solutions for
y = -x² - 5x + 12

• -4.9 and -0.1
• -8.54 and 8.54
• -0.45 and 3.55
• -6.77 and 1.77

Multiple Choice

Use the quadratic formula to find the solutions for

y = 3x³ + 8x - 1

• 0.1167 and -2.7833

• .7 and -16.7

• .35 and -8.35

• 0.2358 and -1.236

Homework: Study for Quiz

Quiz Topics:

1. Solving Using the Quadratic Formula

2. The Discriminant

3. Graphing in Vertex Form