Quadratic Functions: Parent, Vertex, Axis of Symmetry

Quadratic Functions: Parent, Vertex, Axis of Symmetry

Introduction

Parent Function

Graph of the Parent Funciton

• The graph is a PARABOLA 

• All other forms of quadratic equations can be traced to this form.
  

• Similar graphical features exist in the other variations

Graphical characteristics of the parent function

Multiple Choice

Which of the following equations matches standard form of a quadratic?

• y = a(x - h)² + k

• y = ax² + bx + c

• ax + by = cy

Main Focus

Vertex and Axis of Symmetry

Vertex and Axis of symmetry

• VERTEX: lowest point or a highest point

• AXIS OF SYMMETRY:  a line about which the parabola is symmetrical (balanced)

Multiple Choice

What is the green dashed line called?

• parabola

• roots or x-intercepts

• axis of symmetry

• line of dashes

Multiple Choice

A parabola has a vertex at (-3,2).

Where is the axis of symmetry?

• y = -2

• x = 3

• y = 2

• x = -3

Multiple Choice

The axis of symmetry line passes through which point?

• y-intercept

• any random point

• vertex

Quick Review

Maximum: top of curve ---- Minimum: bottom of curve

Multiple Choice

What is the green dot on the parabola called?

• Root

• Zero

• Minimum

• Maximum

Finding Vertex from Standard Form

https://www.youtube.com/watch?v=WTk4m6Ovv9s

Standard Form / Vertex Form

• Standard Form: 1.  Identify a and b values

• 2. the axis of symmetry is x =  $-\frac{b}{2a}$  

• 3.  plug in x to get y value

• Vertex Form: 

• 1.  Identify h and k

• 2.  the axis of symmety is h

• 3. the vertex is (h, k)

Multiple Choice

If given the equation

y = 3(x + 5)² - 4,

what is the vertex of the parabola?

• (-15, -4)

• (5, -4)

• (-5, -4)

• (15, -4)

Multiple Choice

Find the vertex. y = x²+ 16x + 71

• V(-8, 3)

• V(-8, 7)

• V(8, 10)

More Practice

Putting it all together

Multiple Choice

 What is the "formula" for finding the axis of symmetry? 

• 
     $y=ax^2+bx+c$  

•  $y=mx+b$  

• $$x=\frac{-b}{2a}$$  

• $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$  

Multiple Choice

The equation for the axis of symmetry line is x = -b/(2a)

• True

• False

Multiple Choice

Given the equation for this parabola:

y=-(x-4)²-3,

does this parabola have a maximum or minimum value?

• Maximum

• Minimum

Multiple Choice

Identify the vertex and whether the graph opens up or down.

• (5, 2); opens up

• (-5, 2); opens up

• (5, 2); opens down

• (-5, 2); opens down

Multiple Choice

Find the vertex of

f(x) = -x² - 4x + 12

• (-2, 16)

• (2, 0)

• (2, 4)

• (-2, 4)