1/5 Alg2: Quadratics

Introduction to Quadratics

The beauty of parabolas

What are quadratics?

Yesterday we took a sneak peak into what we will be talking about. A quadratic function is a special type of function in which the graph is always a parabola (the shape of the letter "u").

Learning Targets

• I can identify a quadratic function in both equation and graph form. 

• I can identify the axis of symmetry and the vertex of a quadratic function.

(Go to Desmos to show transformations)

Poll

The general vertex form of a parabola is  $f\left(x\right)=a\left(x-h\right)^2+k$  where

 $\left(h,\ k\right)$   is the vertex of the parabola. 

What is the vertex of the parabola defined by  $f\left(x\right)=2\left(x-3\right)^2+4$  ?

• (2, -3)

• (3, 4)

• (-3, 4)

• (2, 4)

Multiple Choice

The general vertex form of a parabola is

 $f\left(x\right)=a\left(x-h\right)^2+k$  where  $\left(h,\ k\right)$  is the vertex. 

What is the vertex of the parabola defined by  $f\left(x\right)=-\left(x-5\right)^2-3$  

• (-1, 0)

• (-5, 3)

• (5, -3)

• (-1, -3)

Multiple Choice

The general vertex form of a parabola is

 $f\left(x\right)=a\left(x-h\right)^2+k$  where  $\left(h,\ k\right)$  is the vertex. 

What is the vertex of the parabola defined by  $f\left(x\right)=-9\left(x+4\right)^2-3$  

• (-4, -3)

• (4, 3)

• (-9, 0)

• (-1, -3)

Multiple Choice

The general vertex form of a parabola is

 $f\left(x\right)=a\left(x-h\right)^2+k$  where  $x=h$  is the AXIS OF SYMMETRY. 

What is the axis of symmetry of the parabola defined by  $f\left(x\right)=-9\left(x+4\right)^2-3$  

•  $x=-4$  
  

•  $x=4$ 

•  $x=-3$  
  

•  $x=0$  
  

Multiple Choice

What is the vertex, (h, k)?

• (0, 0)

• (1, 0)

• (-1, 1)

• (1, 1)

Multiple Choice

What is the axis of symmetry,  $x=h$  ?

•  $x=0$  
  

•  $x=-3$ 

•  $x=-1$  
  

•  $x=-4$  
  

Multiple Choice

What is the vertex, (h, k)?

• (0, 0)

• (0, -1)

• (-1, 0)

• (-1, -1)

Excellent work! Where do you see parabolas in your life? Think to yourself, then we'll answer on the next slide.

Open Ended

Where do you see parabolas in your life?