The graph of any quadratic function is called a parabola.
Parabolas are shaped like cups , as shown in the graph below. If
the coefficient of x2is positive , the parabola opens upward;
otherwise, the parabola opens downward. The vertex (or turning
point) is the minimum or maximum point.
The Standard Form of a
• The quadratic function
• f (x) = a( x - h)2 + k, a ≠ 0
• is in standard form. The graph of f is a parabola
whose vertex is the point (h, k). The parabola is
symmetric to the line x = h. If a > 0, the parabola
opens upward; if a < 0, the parabola opens
Graphing Parabolas With Equations
in Standard Form
• To graph f (x) = a(x - h)2 + k:
2. De termine whether the parabola opens upward or
downward. If a > 0, it opens upward. If a < 0, it opens
3. Determine the vertex of the parabola. The vertex is (h,
4. Find any x-intercepts
by replacing f (x) with 0. Solve
the resulting quadratic equation for x .
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