Name __________________________ 5.2 Graph Quadratic Functions in Vertex Form Write your questions and thoughts here!
Lesson goal – You will need a graphing calculator for this lesson. Another useful form for quadratic functions is ___________________________, y = a(x – h)2 + k, where a ≠ 0. In this form it is easy to identify _________________and __________________ of a quadratic function. The Graph of Vertex Form The graph of ____________________ is the parabola __________ translated ____ units horizontally and ____ units vertically. Properties of Quadratic Functions in Vertex Form The graph of y = a(x – h)2 + k is a parabola with these characteristics: •
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graph opens up when ___________________________ graph opens down when _________________________ The vertex is _________ The axis of symmetry is _________ You Try – For the quadratic function y = ‐3(x – 4)2 + 6 a. Does the graph open up or down? __________ b. What are the coordinates of the vertex? _______________ c. What is the axis of symmetry? _____________ To graph a quadratic function in vertex form • Determine _____________________________________________ • Plot _______________________ • Draw _____________________________ • Plot _______________ using any x‐value • _______________ the point across the axis of symmetry or • Use ______________________ to plot a 2nd and 3rd point • Draw a ____________________ through the points 1 Name __________________________ 5.2 Graph Quadratic Functions in Vertex Form Examples Graph y = (x +2)2 – 3. Label the vertex and the axis of symmetry. Graph y = ‐ (x + 3)2 + 4. Label the vertex and the axis of symmetry. You Try – Graph y = 4(x – 1)2 + 5. Label the vertex and the axis of symmetry. Summarize Your Notes ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ 2 5.2 Practice – Graph Quadratic Functions in Vertex Form Textbook Pg. 245‐249 What is the vertex of the graph of the function? 1. y = 3(x + 2)2 – 5 2. y = ‐4(x + 6)2 – 12 Graph the function. Label the vertex and axis of symmetry. 3. y = (x – 3)2 4. y = 3(x – 7)2 – 1 ଵ
5. f(x) = ‐2(x – 1)2 – 5 6. y = (x – 3)2 + 2 ଶ
Write the quadratic function in standard form. 7. f(x) = ‐(x + 6)2 + 10 8. g(x) = 12(x – 1)2 + 4 5.2 Practice – Graph Quadratic Functions in Vertex Form Textbook Pg. 245‐249 Graph the function. Label the vertex and the axis of symmetry. ଶ
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9. y = (x – )2 + ଷ
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10. y = ‐0.25(x – 5.2)2 + 8.5 Name __________________________ 5.2 Application 1. Mr. Vining has been working on his diving skills for many years. The path that he follows when diving is given by y = ‐0.4(x – 4)2 + 14 where x is the horizontal distance (in feet) from the edge of the diving board and y is the height (in feet). a. Graph the model. Label the vertex and the axis of symmetry. b. What is Mr. Vining’s maximum height? 2. Although a football field appears to be flat, its surface is actually shaped like a parabola so that rain runs off to either side. The cross section of a field with synthetic turf can be modeled by y = ‐0.000234(x – 80)2 + 1.5 where x and y are measured in feet. a. What is the field’s width? b. What is the maximum height of the field’s surface?