Writing quadratic functions

Interactive Lesson

Writing Quadratic Equations

Have your notebook nearby to show your work!

Forms of Quadratic Functions

• Vertex Form:  

   $y=a\left(x-h\right)^2+k$  

• Standard Form:       $y=ax^2+bx+c$  

• Root Form:  $y=x\left(x-r_1\right)\left(x-r_2\right)$  
  
  

Multiple Choice

What form of a quadratic is given?

 $f\left(x\right)=2x^2+3x-4$  

• Vertex Form

• Standard Form

• Root Form

Multiple Choice

What form of a quadratic is given?

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

• Vertex Form

• Standard Form

• Root Form

Fill in the Blank

Given the equation

 $f\left(x\right)=-5\left(x-2\right)^2-4$ , what is the vertex for the parabola? 
Write your answer as a coordinate point. (x, y)

Multiple Choice

Lets do another problem just to make sure we've got this.

Find the equation of a parabola that has a vertex at (2, -7) and goes through the point (3, -4).

• $y=\frac{3}{25}\left(x+2\right)^2-7$

• $y=3\left(x-2\right)^2-7$

• $y=3\left(x+2\right)^2-7$

• $y=\left(x-2\right)^2-7$

Multiple Choice

Find the equation for a parabola that has a vertex at (3, 4) and goes through the point (2, 2).

• $y=\left(x-3\right)^2+4$

• $y=-\frac{2}{25}\left(x+3\right)^2+4$

• $y=-2\left(x-3\right)^2+4$

• $y=-2\left(x+3\right)^2-4$