3.1 Writing Quadratic Equations

3.1 Writing Quadratic Equations

Have your notebook nearby to show your work!

Forms of Quadratic Functions

• Vertex Form:  

   $y=a\left(x-c\right)^2+d$  

• 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

Multiple Choice

What form of a quadratic is given?

 $f\left(x\right)=-\left(x+2\right)\left(x-5\right)$  

• Vertex Form

• Standard Form

• Root Form

Multiple Choice

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

• $y=\left(x-3\right)^2+4$

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

• $y=-2\left(x-3\right)^2+4$

• $y=-2\left(x+3\right)^2-4$

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).

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

• $y=3\left(x-2\right)^2-7$

• $y=3\left(x+2\right)^2-7$

• $y=\left(x-2\right)^2-7$

Fill in the Blanks

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

Write the equation for a parabola that has the roots x=2 and x=4 and goes through the point (0, -4).

• $y=-\frac{1}{2}\left(x+2\right)\left(x+4\right)$

• $y=-\frac{1}{2}\left(x-2\right)\left(x-4\right)$

• $y=\left(x-2\right)\left(x-4\right)$

• $y=-\frac{1}{2}\left(x-2\right)\left(x-3\right)$

Multiple Choice

Lets do another one just to make sure we get this down.

Write the equation for a parabola that has the roots x=-3 and x=1 and goes through the point (-2, -9).

•  $y=3\left(x-3\right)\left(x+1\right)$ 

•  $y=\left(x+3\right)\left(x-1\right)$ 

•  $y=\left(x-3\right)\left(x+1\right)$ 

•  $y=3\left(x+3\right)\left(x-1\right)$ 

Multiple Select

Given the equation

 $f\left(x\right)=2\left(x-4\right)\left(x+6\right)$ , determine the roots (zeros) for this parabola.

Select all that apply.

• x = -6

• x = -4

• x = 2

• x = 4

• x = 6

Multiple Choice

Write the equation of a parabola that goes through (-2, 3), (-1, 0), and (1, 6).

• $y=x^2+2x+3$

• $y=2x^2+3x+1$

• $y=3x^2+3x$

• $y=3x^2+2x+3$

Multiple Choice

Alright, one more time. 

Write the equation of a parabola that goes through (7, -4), (5, -1), and (1, -1).

•  $y=-0.25x^2+15x+2.25$ 

•  $y=0.25x^2-1.5x+2.25$ 

•  $y=-0.25x^2+1.5x-2.25$ 

•  $y=-x^2+x-2$ 

This is for a grade! You must make a 70 on this lesson to receive credit.

At the end of the unit, I will see what lessons you have completed. If you completed all of them, it's an easy 100 for a quiz.