Graphing Quadratics in Standard Form

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Presentation transcript:

Graphing Quadratics in Standard Form Section 4.2 Graphing Quadratics in Standard Form

Use a Formula for Finding the Vertex of a Parabola. Objective 1 Use a Formula for Finding the Vertex of a Parabola.

Vertex Formula The graph of f(x) = ax2 + bx + c, when a ≠ 0, is a parabola with vertex

Example 1 Find the vertex of the graph of

Example 1 Find the x intercepts of the graph of

Example 1 Graph

Example 2 Graph f(x) = 3x2 – 4x - 10

Example 3 Graph f(x) = x2 + 3x - 10

Find the Minimum or Maximum Value of a Quadratic Function. Objective 1 Find the Minimum or Maximum Value of a Quadratic Function.

Finding a Maximum or Minimum The quadratic function whose graph is a parabola that opens upward has a minimum value, and the quadratic function whose graph is a parabola that opens downward has a maximum value. The f(x)- or y-value of the vertex is the minimum, or maximum value of the function.

Example The Utah Ski Club sells calendars to raise money. The profit P, in cents, from selling x calendars is given by the equation P(x) = 360x – x2. What is the maximum profit the club will earn? Continued