Quadratic Functions Different Forms applet

Investigate different forms of quadratic functions. Move the sliders in order to find out what each form 'reveals' about the graph.

FACTORED FORM

What does the factored form tell us about the graph of the function? Why is it useful?

VERTEX FORM

What does the vertex form tell us about the graph of the function? Why is it useful?

EXPANDED/STANDARD FORM

What does the expanded (also called standard) form tell us about the graph of the function? Why is it useful?

What are the zeros of the function f given below (in three different forms)

[br][math]f\left(x\right)=x^2-2x-3[/math][br][math]f\left(x\right)=\left(x+1\right)\left(x-3\right)[/math][br][math]f\left(x\right)=\left(x-1\right)^2-4[/math]

[math]x_1=1,x_2=-3[/math] [math]x_1=-2,x_2=-3[/math] [math]x_1=-1,x_2=-4[/math] [math]x_1=-1,x_2=3[/math]

Sketch quadratic functions with given properties

In the 'Input' window, enter examples of quadratic functions with given properties:[br][br]a) function f has vertex at (-2, -3)[br][br]b) function g has zeros at -4 and 5[br][br]c) function h has y-intercept at (0,2)[br][br]d) function p has at least one of the zeros at x=0