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The graph of a quadratic function is a parabola. The standard form of a quadratic function is written as
. If
,
the parabola opens upward; if
,
it opens downward. To graph the function, first find the vertex by:
1. Either completing the square to rewrite the function in the form
(the vertex is (h, k)) or finding the line of symmetry using the equation
,
which calculates the x-coordinate of the vertex, and then finding the y value of the vertex by substituting the value of x into the original equation.
2. Then find the x- and y-intercepts of the graph. To find the x-intercepts, solve the quadratic equation,
To find the y-intercept of
,
find f(0).
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