Introduction to Quadratic Functions

Quadratic Functions

Monday Dec. 14, 2020

Multiple Choice

Warm up:

What are the factors of 100x² + 120x + 36

• can't be factored

• 4(5x+3)²

• 4(5x + 3) (5x - 3)

Quadratic Functions

What are they? How do we solve them?

What are quadratic functions?

Quadratic functions just means you have an expression raised to the second power (ax² +bx +c --> where a, b, and c are constants)

So... what does this have to do with anything?

All the skills we've been learning and practicing the last two months are all linked to quadratics.

Factoring, in any form, is how we are going to find the zeros and other intercepts of quadratic functions on graphs.

(if you are still struggling with factoring, this next piece might help you understand it a little better (yes, I know I've said that before, but it was true then and it's true now))

Let's start here -->

This, is a quadratic function.

This shape is called a parabola. Pronounced per - ab - oh - lah

Finding Zeros

The zeros of a function are the places where the graph crosses the x-axis (in linear functions we call these the x-intercepts).

With quadratics you can have 0, 1, or 2 depending on the graph.

You can visually see these, AND mathematically calculate where these points happen.

Calculating Zeros (x-intercepts)

To calculate the zeros of a quadratic function, et each factor equal to 0 and solve for x. Then write your answer as an ordered pair (x, 0) *You will have a number for x every time, it's the answer you get*.

Example: y = (x - 8)(8x - 5)

x - 8 = 0

x = 8

(8, 0)

8x - 5 = 0

8x = 5

x = 5/8

(5/8, 0)

Multiple Choice

Find the zeros of this quadratic: y = (x - 3)(5x + 6)

• (-3, 0) and (5x, 0)

• (3, 0) and

  $$\left(-\frac{6}{5},0\right)$$
  

• (0,3)

• There aren't any

Multiple Choice

Find the zeros:

$$y=x^2+6x-7$$  Remember to factor first

• (7, 0) and (-1, 0)

• Can't factor so can't find zeros

• (-7, 0) and (1, 0)

Go Practice

There is a worksheet to practice finding zeros in Google Classroom. Please show your work (I know it's repetitive, but please show each step each time)