Interactive Lesson on Quadratic Function

Quadratic Functions

Try the activating question to

the right

Factoring when a = 1

• Find factors of c

• Which ones add to b?

• Write as (x___)(x___)

• Ex: x² + 9x + 20

Multiple Choice

For the quadratic function x² - 17 + 30, which of these would be a factor:

• (x + 5)

• (x + 15)

• (x - 15)

• (x + 2)

Factoring when a ≠ 1

• Multiply a*c and make a 1

• Find factors of c

• Which ones add to b?

• Divide factors by a

• Multiply by a and distribute

• Ex: 6x² + 11x - 10

Multiple Choice

Which of the following is a correct factor for

3x² + 13x + 12

• (x + 4)

• (3x + 3)

• (3x + 4)

• (x + 6)

Completing the Square

• Converting from standard form to vertex form

• Move c to the other side

• h = (1/2)b

• Add h² on both sides

• Move constant back

• Ex: x² - 18x + 72

Multiple Choice

Write x² + 4x - 12 in vertex form by completing the square

• (x + 4)² + 2

• (x + 2)² - 16

• (x - 4)² + 16

• (x -2)² + 16

Solving by Completing the Square

• Move c to the other side

• h = (1/2)b

• Add h² on both sides

• Take the square root of both sides

• Ex: x² - 18x + 72

Multiple Choice

What are the solutions to this quadratic function:

x² + 4x - 12

• {2, 6}

• {-2, -6}

• {-2, 6}

• {2, -6}

Quadratic Formula

• Ex: 6x² + 7x - 8

Multiple Choice

Solve for x:

x² + 14x + 7

• $$-7\pm\sqrt{14}$$

• $$7\pm\sqrt{24}$$

• $$-7\pm\sqrt{42}$$

• $$7\pm\sqrt{46}$$