3.1 Writing Quadratic Equations

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

• Factored 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

• Factored 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

• Factored 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 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

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

Hint: Create a table in desmos

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).

• $$y=-0.25x^2+15x+2.25$$

• $$y=0.25x^2-1.5x+2.25$$

• $$y=-0.25x^2+1.5x-2.25$$

• $$y=-x^2+x-2$$

Multiple Choice

Find the best fitting quadratic model for the data given.

• $$1.2x^2+13x+504.3$$

• $$12x^2+13x+504.3$$
  

• $$0.12x^2+1.3x+504.3$$