Explore the Equation grapher simulation (below) for several minutes:
The axes of the graph are indicated by black lines and labels x and y.
The black "tick" marks represent a magnitude of 1 from the origin (0,0).
The polynomial function f(x)=ax2+bx+c is represented by the red line.
Try clicking around
Try dragging objects
Try sliding sliders
When you have finished exploring try the multichoice question. Once you have completed the multichoice question try one of the main activities.
While you were exploring you may have noticed that the function curves when you give the coefficient a a value different from zero. Which values for the polynomial coefficients best describe a function f(x) that has outputs of
f(0) = 1
f(-1) = 0
f(1) = 0
Think about the affect of each coefficient on the output of the function. Can you have the same output from the function if a=0?
(a) a=1, b=0, c=1
Incorrect, this polynomial function has outputs of f(0)=1, f(-1)=2, and f(1)=2.
(b) a=0, b=1, c=1
Incorrect, this polynomial function has outputs of f(0)=1, f(-1)=0, and f(1)=2.
(c) a=-1, b=0, c=1
Absolutely correct, this polynomial function has outputs of f(0)=1, f(-1)=0, and f(1)=0.
When a function f(x) has the same output for positive and negative values of x, it is symmetric about the y-axis (vertical axis) and often called an even function.