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Graphing Quadratic Functions in Standard From Section 7.2.

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Presentation on theme: "Graphing Quadratic Functions in Standard From Section 7.2."— Presentation transcript:

1 Graphing Quadratic Functions in Standard From Section 7.2

2 Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 2 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Vertex Formula To find the vertex of the graph of a quadratic function 1.Find the x-coordinate of the vertex by using the vertex formula 2. Find the y-coordinate of the vertex by evaluating f at the value found in step 1. That is, find − b 2a. Process

3 Lehmann, Intermediate Algebra, 4ed Find the vertex of the graph of a = 1, b = –4, and c = 7 Find the x-coordinate by substituting a and b into the formula Find the y-coordinate by finding f (2): So, the vertex is (2, 3) Section 7.2Slide 3 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Find the Vertex Example Solution

4 Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 4 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function Sketch a graph of a = 2, b = 10, and c = 7 Find the x-coordinate of the vertex: Find the y-coordinate of the vertex: So, the vertex is (–2.5, –5.5) Find additional input-output pairs: Example Solution

5 Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 5 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function ExampleSolution Continued

6 Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 6 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function Sketch a graph of a = –2.2, b = 6.1, and c = 1.4 Find the x-coordinate of the vertex: Find the y-coordinate of the vertex: So, the vertex is (1.39, 5.63) Find additional input-output pairs: Example Solution

7 Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 7 Method 2: Graphing by Using the Vertex Formula to Find the Vertex Using the Vertex Formula to Graph a Quadratic Function ExampleSolution Continued

8 Lehmann, Intermediate Algebra, 4ed Section 7.2Slide 8 Minimum of Maximum Value Maximum of Minimum Value of a Function For a quadratic function whose graph has vertex (h, k), If a < 0, then the parabola opens downward and the maximum value of the function is k If a > 0, then the parabola opens upward and the minimum value of the function is k Property

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