Math 102 Lesson 3.2 Part I

​Math 102 - Lesson 3.2

​Quadratic Functions and Graphs

​Quadratic Function

​Earlier we saw that the graph of y=x² is a parabola.

The function P(x) = x² is the simplest form of a quadratic function.

Multiple Choice

Describe the shifts of the graph

$$f\left(x\right)=\left(x-3\right)^2+4$$

• left 3 down 4

• right 3 up 4

• left 3 up 4

• right 3 down 4

Multiple Choice

What is the equation of the graph shown?

• y=(x-4)² + 1

• y = (x + 1)² - 4

• y = (x + 4)² - 1

• y = (x - 4)² + 1

Math Response

What are the factors of x² -10x + 25?

Type answer here

Correct Answer: \left(x-5\right)^2

Deg^°

Rad

Math Response

What are the factors of x² + 8x + 16?

Type answer here

Correct Answer: \left(x+4\right)^2

Deg^°

Rad

Math Response

What are the factors of x² + 12x + 36?

Type answer here

Correct Answer: \left(x+6\right)^2

Deg^°

Rad

​Example 1

​P(x) = x² - 2x - 15

P(x) + 15 = x² - 2x

P(x) + 15 + 1 = x² - 2x + 1

P(x) + 16 = (x - 1)²

P(x) = (x - 1)² - 16

​Write the function in the form y = a(x-h)²+k

​1. Add 15 to both sides

2. Take (1/2*b) and square it. Add result to both sides

3. Factor the right side

4. Subtract 16 back to other side

Math Response

Write the function in the form y = a(x-h)² + k

P(x) = x² + 4x

Type answer here

Correct Answer: \left(x+2\right)^2-4

Deg^°

Rad