Quadratic graph analysis
Quadratic equation graph analysis, comparing the general form, factored form and completed square form.
1) Looking at the General equation, answer fully:
a. What’s the effect of changing the coefficient “a”?
b. What’s the effect of changing the coefficient “c”?
c. What can you notice about the effect of changing the coefficient “b”?
2) Looking at the Completed Square equation, answer fully:
a. Is the effect of changing “a” different or the same as in the General form?
b. What does the coefficients “h” and “k” represent in this equation form?
c. What are the effects of changing “h” and “k” on the graph?
d. What can you tell about the effects of changing “h” and “k” on the Y-intercept’s value?
e. Can you figure a mathematical relation between “c”, “h” and “k”?
3) Looking at the Factored equation, answer fully:
a. Is the effect of changing “a” different or the same as in the General form?
b. What does the coefficients “x1” and “x2” represent in this equation form?
c. What happens when “x1” and “x2” are the same?
d. What happens when “x1” and “x2” are the same but with opposite signs?
e. Can you figure a mathematical relation between “x1”, “x2” and the vertex?
f. Can you figure a mathematical relation between “x1”, “x2” and “c”?