Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic.

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Presentation transcript:

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. Graph Quadratic Functions in Vertex & Intercept Form

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. VERTEX FORM OF QUADRATIC EQUATION y = a(x - h) 2 + k  The vertex is (h, k).  The axis of symmetry is x = h.

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. Example 1 Graph a quadratic function in vertex form Graph Solution 1.Identify the constants a = ____, h = ___, and k = ____. Because a > 0, the parabola opens ____. 2.Plot the vertex (h, k) = (___, ___) and draw the axis of symmetry at x = ____. 3.Use the pattern for the parabola to plot the other points. a = ____, so the graph is going up half as fast as normal. 4.Draw a parabola through the plotted points.

Graph the function. Label the vertex and axis of symmetry. You Try It!

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. INTERCEPT FORM OF QUADRATIC EQUATION y = a(x - p)(x - q)

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. Example 2 Graph a quadratic function in intercept form Graph Solution 1.Identify the x-intercepts. Because p = ____ and q = ____, the x-intercepts occur at the points (___, 0) and (___, 0). 2.Find the coordinates of the vertex. 4.Draw a parabola through the vertex and the points where the x-intercepts occur. So, the vertex is (___, ___).

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. Graph the function. Label the vertex, axis of symmetry, and x-intercepts. You Try It!

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. Changing quadratic functions from intercept form or vertex form to standard form. FOIL Method: To multiply two expressions that each contain two terms, add the products of the First terms, the Outer terms, the Inner terms, and the Last terms. Example: F O I L F O I L (x + 4)(x + 7) = x 2 + 7x + 4x + 28 (x + 4)(x + 7) = x 2 + 7x + 4x + 28 = x x + 28

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. Example 4 Change quadratic function to standard form Original function. Solution Multiply using FOIL. Combine like terms. Distributive property.

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. Write the quadratic function in standard form. You Try It!

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. Example 5 Change quadratic function to standard form Original function. Solution Rewrite (x + 2) 2. Combine like terms. Distributive property. Multiply using FOIL. Combine like terms.

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. Write the quadratic function in standard form. Write the quadratic function in standard form. You Try It!

Essential Question: How do you graph a quadratic function in vertex and intercept form? Students will write a summary on the steps to graphing quadratic functions in vertex & intercept form. HOMEWORK TextbookTextbook Pg ,8,14,20,29,25,33,34 Write your Summary to the Essential Question Write your Summary to the Essential Question