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# 5.8 Modeling with Quadratic Functions

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### 5.8 Modeling with Quadratic Functions

1. 1. 5.8 Modeling withQuadratic Functions
2. 2. Writing a Quadratic in Vertex Form: y=a(x-h)2 + k Given the vertex and a point on the parabola, we can write the function. Example: (4, 1) vertex: (2, -3)
3. 3. Your Turn! Write an equation of the parabola with vertex (-1, 4) that goes through the point (2, 7).
4. 4. Writing a Quadratic inIntercept Form: y=a(x-p)(x-q) Given the x-intercepts and a point on the parabola, we can write the function. Example: (-1, 2)
5. 5. Your Turn! Write an equation of the parabola with x-intercepts 1 and 4 that goes through the point (2, -6).
6. 6. Writing a Quadratic in Standard Form: y = ax2 + bx + c Given three points on the parabola, we can write the function.1. Substitute each ordered pair into y = ax2 + bx + c to get three equations in a, b, and c.2. Solve the 3-variable system to find a, b, and c.3. Write in standard form.
7. 7. Example Write a function in standard form for the parabola passing through the points (2, -2), (3, 4), and (0, -2).
8. 8. Your Turn! Write a function in standard form for the parabola passing through the points (-2, 0), (-1, 2), and (3, 0).
9. 9. Finding a Quadratic Model for a Data Set  You can use a graphing calculator   Example:  A study compared the speed x (in mph) and the avg. fuel economy y (in miles per gallon) for cars. Find a quadratic model for the data and find the speed that maximizes fuel economy.Speed, x 15 20 25 30 35 40 45 50 55 60 65 70Fuel 22.3 25.5 27.5 29.0 28.8 30.0 29.9 30.2 30.4 28.8 27.4 25.3Economy, y