Introduction to Quadratic Functions

4.1 Intro to Quadratic Functions

Parabola

Examples of Quadratic Functions

•  $f\left(x\right)=ax^2+bx+c$  

Multiple Choice

Which of the following is not a quadratic function?

• $$f\left(x\right)=x^2$$

• $$f\left(x\right)=-2x^2+5x+1$$

• $$f\left(x\right)=3x^2-9$$

• $$f\left(x\right)=4x-1$$

• $$f\left(x\right)=4x^2-x$$

Axis of Symmetry

 $x=\frac{-b}{2a}$  

Vertex

Maximum when a < 0

Minimum when a > 0

How to find the vertex

Multiple Choice

Find the vertex of

$$f\left(x\right)=x^2+2x-3$$  

• (-1, -4)

• (-1, -6)

• (1, 0)

• (-2, -3)

Summary

• Standard Form:

   $f\left(x\right)=ax^2+bx+c,\ \ a\ne0$  

• if a<0, parabola opens down

• if a>0, parabola opens up

• Equation for Axis of Symmetry:  $x\ =\ \frac{-b}{2a}$  

• To find vertex, find  $f\left(\frac{-b}{2a}\right)$  

• Next Lesson... we will learn how to find the x and y-intercepts!