Intro to Quadratics...the Parabola

Intro to Quadratics...the Parabola

Objectives

• The students will learn that the graph created by a quadratic function is called a parabola

• The students will be able to identify the parts of a parabola

 $f\left(x\right)=x^2$  

• The vertex is at (0, 0)

• This parabola opens UP and has a MINIMUM value of 0

• The DOMAIN is All Real Numbers

• The RANGE is  $y\ge0$  

• There is one SOLUTION at x=0

• The axis of symmetry is x = 0

• The y-intercept is 0

 $y=-\left(x-2\right)^2+1$  

• The vertex is at (2, 1)

• This parabola opens DOWN and has a MAXIMUM value of 1

• The DOMAIN is All Real Numbers

• The RANGE is  $y\le1$  

• There are 2 SOLUTIONS at (1, 0) and (3, 0)

• The axis of symmetry is x = 2

• The y-intercept is -3

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

• The vertex is at (3, 4)

• This parabola opens UP and has a MINIMUM value of 4

• The DOMAIN is All Real Numbers

• The RANGE is  $y\ge4$  

• There are NO REAL SOLUTIONS

• The axis of symmetry is x = 3

• The y-intercept is 13

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

• The vertex is at (-4, -2)

• This parabola opens DOWN and has a MAXIMUM value of -2

• The DOMAIN is All Real Numbers

• The RANGE is  $y\le-2$  

• There are NO REAL SOLUTIONS

• The axis of symmetry is x = -4

• The y-intercept is -18

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

• The vertex is at (4, 0)

• This parabola opens DOWN and has a MAXIMUM value of 0

• The DOMAIN is All Real Numbers

• The RANGE is  $y\le0$  

• There is 1 solution at (4, 0)

• The axis of symmetry is x = 4

• The y-intercept is -16

 $f\left(x\right)=\left(x+2\right)^2-6$  

• The vertex is at (-2, -6)

• This parabola opens UP and has a MINIMUM value of -6

• The DOMAIN is All Real Numbers

• The RANGE is  $y\ge-6$  

• There are 2 solutions at approximately (0.45, 0) and (-4.45, 0)

• The axis of symmetry is x = -2

• The y-intercept is -2

Multiple Select

Describe this parabola. Check all that apply

• Opens Up

• Opens Down

• Domain is All Real Numbers

• Range $y\ge4$
  

• Range $y\le4$

Multiple Select

Describe this parabola. Check all that apply.

• It has a MINIMUM value

• It has a MAXIMUM value

• It has NO REAL SOLUTIONS

• The y-intercept is 3

• It has 2 solutions

Multiple Choice

The axis of symmetry is a ____ line

• Horizontal

• Vertical

Multiple Choice

How many REAL solutions does this have?

• None

• One

• Two

Multiple Choice

Parabolas that open UP will always have a ...

• MAXIMUM value

• MINIMUM value

Multiple Select

x-intercepts are also known as (check all that apply) ...

• Roots

• Solutions

• y-intercepts

• Zeros

Fill in the Blank

There are ____ solutions to this quadratic

Fill in the Blank

This parabola opens ___

Multiple Choice

The DOMAIN of the quadratic shown is

•  $y\ge-4$  

• All Real Numbers

Multiple Choice

The RANGE of the quadratic shown is

•  $y\ge-4$  

• All Real Numbers

•  $y\le-4$