Graphing Quadratic Functions
The Graph of f(x) = Ax^{2} + Bx + C
Example 1The graph of y = 0.5x^{2} is shown. Assume that the coefficient of x^{2} for all
three graphs is 0.5.
a. Find the equation of Parabola A.
b. Find the equation of Parabola B.
Solution
a. Parabola A is the graph of f(x) = 0.5x^{2} shifted down 4 units.
So, it is the graph of the function f(x) = 0.5x^{2}  4.
b. Parabola B is the graph of f(x) = 0.5x^{2} shifted up 2 units.
So, it is the graph of the function f(x) = 0.5x^{2} + 2.
Example 2
Graph the functions:
a. f(x) = x^{2}
b. f(x) = x^{2} + 4
c. f(x) = x^{2}  3
Solution
a. The function f(x) = x^{2} has the same shape as f(x) = x^{2} but, because
of the negative sign, it opens downward. To see this, we can calculate
and plot a few ordered pairs.
x 
f(x) = x^{2} 
(x, y) 
2 1
0
1
2 
f(2) = (2)^{2} = 4 f(1) = (1)^{2} = 1
f(0) = (0)^{2} = 0
f(1) = (1)^{2} = 1
f(2) = (2)^{2} = 4 
(2, 4) (1, 1)
(0, 0)
(1, 1)
(2, 4) 
b. The graph of f(x) = x^{2} + 4 has the same shape as f(x) = x^{2} but is
shifted up 4 units.
c. The graph of f(x) = x^{2}  3 has the same shape as f(x) = x^{2} but is
shifted down 3 units.
