Analyzing Graphs of Quadratic Functions
Author: John Maharry
Date: January 9,2007

There are two parabolas below.  The equation of the red parabola is written in intercept form and the equation of the blue parabola is written in vertex form.

Click on the parabola worksheet to start. Then you can move the sliders to change the parameters and the graphs. Explore the relationships between the forms of the functions and the graphs.

y=a*(x-h)²+k    Vertex Form

y=a*(x-x1)*(x-x2)   Intercept Form

a = 0.7000000000000002 (slider from -3 to 3, step 0.1)
X1 = -4 (slider from -20 to 20, step 0.1)
X2 = 3.200000000000003 (slider from -20 to 20, step 0.1)
h = 3.200000000000003 (slider from -20 to 20, step 0.1)
k = -8 (slider from -20 to 20, step 0.1)
P: (h, k)
a_b = 0.9000000000000004 (slider from -3 to 3, step 0.1)
d: y = a_b (x - h)² + k
T1: "y = " + a + "(x - (" + X1 + ") )(x - (" + X2 + ") )"
T2: "y = " + a_b + " (x - (" + h + ") )^2 + " + k
c_1: y = a (x - X1) (x - X2)
X2_1 = Intersect(c_1, xAxis, 1)
X1_1 = Intersect(c_1, xAxis, 2)