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Mastering Quadratic Functions and Models for Effective Problem Solving

Learn how to write quadratic functions in vertex, intercept, and standard form with practical examples and exercises for comprehensive understanding. Enhance your skills in modeling parabolas using various methods. Practice exercises included.

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Mastering Quadratic Functions and Models for Effective Problem Solving

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  1. Monday, November 1 Essential Questions • How do I write quadratic functions and models?

  2. 7.2 Write Quadratic Functions and Models Write a quadratic function in vertex form Example 1 Write a quadratic function whose graph has a vertex (-2, -3) and passes through the point (0, 5). Solution Vertex form Substitute for h and k. Use the point (___, ___) to find a. Substitute for x and y. Solve for a. A quadratic function for the parabola is __________________.

  3. 7.2 Write Quadratic Functions and Models Checkpoint. Complete the following exercise. • Write a quadratic function whose graph has vertex (2, 1) and passes through the point (0, 4).

  4. 7.2 Write Quadratic Functions and Models Write a quadratic function in intercept form Example 2 Write a quadratic function whose graph has x-intercepts -3 and 2 and passes through the point (-2, -4). Solution Intercept form Substitute for p and q. Use the point (-2, -4) to find a. Substitute for x and y. Solve for a. A quadratic function for the parabola is __________________.

  5. 7.2 Write Quadratic Functions and Models Checkpoint. Complete the following exercise. • Write a quadratic function whose graph has x-intercepts -4 and 2, and passes through the point (3, 21).

  6. 7.2 Write Quadratic Functions and Models Write a quadratic function in standard form Example 3 Write a quadratic function in standard form for the parabola that passes through the points (-2, -6), (0, 6), and (2, 2) . Substitute the coordinates of each point into y = ax2 + bx + c to obtain a system of three equations. Substitute for x and y. Equation 1 Substitute for x and y. Equation 2 Substitute for x and y. Equation 3

  7. 7.2 Write Quadratic Functions and Models Write a quadratic function in standard form Example 3 Write a quadratic function in standard form for the parabola that passes through the points (-2, -6), (0, 6), and (2, 2) . Rewrite the system as a system of two equations. Substitute for c. Revised Equation 1 Substitute for c. Revised Equation 3

  8. 7.2 Write Quadratic Functions and Models Write a quadratic function in standard form Example 3 Write a quadratic function in standard form for the parabola that passes through the points (-2, -6), (0, 6), and (2, 2) . Solve the system consisting of revised Equations 1 and 3. Revised Equation 1 Revised Equation 3 Add equations. Solve for a. So, ___________=_____, which means b = ___. A quadratic function for the parabola is _____________________.

  9. 7.2 Write Quadratic Functions and Models Checkpoint. Complete the following exercise. • Write a quadratic function in standard form for the parabola that passes through the points (-1, -5), (2, 1), and (3, -1) .

  10. 7.2 Write Quadratic Functions and Models Pg. 266, 7.1 #1-11

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