Math 102 Lesson 3.2 Completing the Square

Math 102
Lesson 3.2

Quadratic Functions and Graphs

​Graphs of Quadratic Functions

​We have used this form before when we talked about transformations.

Remember, that h shifts the graph horizontally "-h" units and k shifts the graph vertically "k" units.

The value of "a" stretches or compresses the graph. Additionally, if "a" < 0, the graph flips vertically and opens down.

Multiple Choice

Describe the shifts of the function

$$f\left(x\right)=\left(x-5\right)^2+3$$

• left 5 and up 3

• right 5 and down 3

• right 5 and up 3

• left 5 and down 3

​What are the coordinates of the y-intercept?



How does this relate to the function?

We want to be able to change from standard form to vertex form for graphing.

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​Completing the Square

​STEPS FOR COMPLETING THE SQUARE

Draw

1). Find the coordinates of the y-intercept

2) Complete the square to rewrite into vertex form

3). Find the coordinates of the vertex

4). Find the reflection of the y-intercept

P(x) = x² - 10x + 21