Writing Quadratic Functions

Interactive Lesson

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Writing Quadratic Equations in Vertex Form

Have your notebook nearby to show your work!

Forms of Quadratic Functions

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).

• $$y=\left(x-3\right)^2+4$$

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

• $$y=-2\left(x-3\right)^2+4$$

• $$y=-2\left(x+3\right)^2-4$$

Multiple Choice

Find the equation for a parabola that has a vertex at (2,3) and goes through the point (4,5).

• $$y=\left(x-4\right)^2+5$$

• $$y=\left(x-2\right)^2+3$$

• $$y=\left(x-4\right)^2-5$$

• $$y=\left(x-2\right)^2-3$$

Multiple Choice

Find the equation for a parabola that has a vertex at (-1,2) and goes through the point (3,4).

• $$y=\frac{1}{8}\left(x-3\right)^2+4$$

• $$y=\frac{1}{8}\left(x+1\right)^2+2$$

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

• $$y=\frac{1}{8}\left(x-1\right)^2+2$$

Multiple Choice

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

Find the equation of a parabola that has x-intercepts at -4 and 3 and passes through the point (2,7)

• $$y=-\frac{7}{6}\left(x-4\right)\left(x-3\right)$$

• $$y=-\frac{7}{6}\left(x+4\right)\left(x-3\right)$$

• $$y=\frac{7}{2}\left(x-4\right)\left(x-3\right)$$

• $$y=\frac{7}{6}\left(x+4\right)\left(x-3\right)$$

Multiple Choice

Find the equation of a parabola that has x-intercepts at -3 and 5 and passes through the point (3,-6)

• $$y=-\frac{1}{2}\left(x+3\right)\left(x-5\right)$$

• $$y=\frac{1}{2}\left(x+3\right)\left(x-5\right)$$

• $$y=\frac{1}{2}\left(x-3\right)\left(x-5\right)$$

• $$y=2\left(x+3\right)\left(x-5\right)$$

Multiple Choice

Find the equation of a parabola that has x-intercepts at 3 and 5 and passes through the point (2,-3)

• $$y=\left(x-3\right)\left(x-5\right)$$

• $$y=-\left(x-3\right)\left(x-5\right)$$

• $$y=-\left(x+3\right)\left(x+5\right)$$

• $$y=\frac{1}{3}\left(x-3\right)\left(x-5\right)$$