Quadratic Features

Quadratic Features

 $y=ax^2+bx+c$  

 $y=a\left(x-h\right)^2+k$  
 $y=\left(x-p\right)\left(x-q\right)$  

This is the graph of a quadratic function

• In green, you see the vertex (highest or lowest point of the graph)

• In red, you see the x-intercepts. A graph doesn't always have x-intercepts.

• Write down the coordinates for each on paper

Multiple Choice

What are the coordinates of the vertex?

• (2,0)

• (2,8)

• (6,0)

• (0,6)

Multiple Select

What are the coordinates of the x-intercepts? (choose all that apply)

• (-2,0)

• (2,8)

• (6,0)

• (0,6)

The graph of a quadratic function is split into two halves

There is an axis of symmetry at x = h (the x-value of the vertex)

Multiple Choice

Considering that the vertex for our function is at (2, 8), what is the equation of the axis of symmetry?

• y=8

• x=8

• y=2

• x=2

This is the parent function of any quadratic graph

 $y=x^2$  
 $y=1\left(x-0\right)^2+0$ 

Its vertex is the LOWEST point, at (0,0) 
It only has one x-intercept, also at (0,0)

If we analyze its transformations...

 $y=1\left(x-0\right)^2+0$  

• there is no negative sign in front of the parentheses, so it is not flipped

• a=1, so it is not stretched or compressed

• h=0 so it does not shift left/right

• k=0 so it does not shift up/down

Multiple Choice

Considering that the vertex for our function is at (0, 0), what is the equation of the axis of symmetry?

• y=0

• x=0

Multiple Choice

In red, you see the parent function,

 $y=\left(x-0\right)^2+0$  In blue, you see the transformation  $y=-\left(x-0\right)^2+0$  How does the negative sign transform the red graph?

• stretch

• move left 3 units

• move up 4 units

• reflect/flip

Multiple Choice

In red, you see the parent function,

 $y=\left(x-0\right)^2+0$  In blue, you see the transformation  $y=2\left(x-0\right)^2+0$  How does a = 2  transform the red graph?

• stretch by 2

• move left 3 units

• move up 4 units

• reflect/flip

Multiple Choice

In red, you see the parent function,

 $y=\left(x-0\right)^2+0$  In blue, you see the transformation  $y=\frac{1}{2}\left(x-0\right)^2+0$  How does a = 2  transform the red graph?

• compress by 1/2

• move left 3 units

• move up 4 units

• reflect/flip

Multiple Choice

In red, you see the parent function,

 $y=\left(x-0\right)^2+0$  In blue, you see the transformation  $y=\left(x-3\right)^2+0$  How does h=3 transform the red graph?

• stretch

• move right 3 units

• move up 4 units

• reflect/flip

Multiple Choice

In red, you see the parent function,

 $y=\left(x-0\right)^2+0$  In blue, you see the transformation  $y=\left(x-0\right)^2+4$  How does k=4 transform the red graph?

• stretch

• move right 3 units

• move up 4 units

• reflect/flip

Multiple Choice

In red, you see the parent function,

 $y=\left(x-0\right)^2+0$  In blue, you see the transformation  $y=-4\left(x+3\right)^2-2$  What are ALL the transformations of the red graph?

• reflect, stretch by 4, shift right 3, and shift down 2

• reflect, compress by 4, shift right 3, and shift down 2

• reflect, stretch by 4, shift left 3, and shift down 2

• reflect, compress by 4, shift left 3, and shift down 2

Poll

Feeling better about transformations?

• definitely

• I still need some practice

• I'm starting to get it

• I'm still lost