Analyzing Graphs of Quadratic Functions
Author: Megan Yanes
Date: October 24, 2006

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

For the two questions below, test using the dynamic graph provided.  Prove or disprove using Algebra.

For any choice of b and c, are there values of h and k that make the two curves coincide?  

For any choice of h and k are there values of b and c that make the two curves coincide?

a = -0.3999999999999986 (slider from -20 to 20, step 0.1)
b = 0.40000000000000213 (slider from -20 to 20, step 0.1)
c = -12.399999999999999 (slider from -20 to 20, step 0.1)
h = 4.400000000000002 (slider from -20 to 20, step 0.1)
k = 6.800000000000001 (slider from -20 to 20, step 0.1)
P: (h, k)
a_b = 0.40000000000000213 (slider from -20 to 20, step 0.1)
d: y = a_b (x - h)² + k
T1: "y = " + a + "(x - " + b + ")(x - (" + c + "))"
T2: "y = " + a_b + " (x - " + h + ")^2 + " + k
c_1: y = a (x - b) (x - c)