How do I write quadratic functions and models? 7.2 Write Quadratic Functions and Models Example 1 Write a quadratic function in vertex form Write a quadratic.

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Presentation transcript:

How do I write quadratic functions and models?

7.2 Write Quadratic Functions and Models Example 1 Write a quadratic function in vertex form Write a quadratic function whose graph has a vertex (  ) 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 __________________.

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

7.2 Write Quadratic Functions and Models Example 2 Write a quadratic function in intercept form Write a quadratic function whose graph has x-intercepts  and  and passes through the point (  ). Solution Intercept form Substitute for p and q. Use the point  to find a. Substitute for x and y. Solve for a. A quadratic function for the parabola is __________________.

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

7.2 Write Quadratic Functions and Models Example 3 Write a quadratic function in standard form Write a quadratic function in standard form for the parabola that passes through the points (  ), (0  ), and (  ). Substitute the coordinates of each point into y = ax 2 + 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

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

7.2 Write Quadratic Functions and Models Example 3 Write a quadratic function in standard form Write a quadratic function in standard form for the parabola that passes through the points (  ), (0  ), and (  ). 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 _____________________.

7.2 Write Quadratic Functions and Models Checkpoint. Complete the following exercise. 3.Write a quadratic function in standard form for the parabola that passes through the points  and 

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