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Evaluate the expression for a = –6 and b = 4. –b2a–b2a Objectives: Graph quadratic functions Section 10-2 Exploring Quadratic Graphs SPI 23E: find the solution to a quadratic equation given in standard form SPI 23F: select the solution to a quadratic equation given a graphical representation –b2a–b2a –4 2(-6) == – = Form of a Quadratic Equation: ax 2 + bx + c Coefficient (a) affects the width of the parabola Constant (c) affects the movement up or down

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Coefficient (b) affects the position of axis of symmetry vertex moves right or left axis of symmetry changes equation of axis of symmetry is x = Role of b in a Quadratic Function

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Explore the Role of b when Graphing a Quadratic Graph the quadratic function y = 2x 2 + 4x – 3. 1.Find the equation of the axis of symmetry. Substitute values into x = 2.Find the coordinates of the vertex using the x value. Substitute x = -1 into the equation to find corresponding y value y = 2x 2 + 4x – 3. = 2(-1) 2 + 4(-1) – 3 = 2 – 4 – 3 = -5 Coordinates of the vertex is (-1, -5)

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Explore the Role of b when Graphing a Quadratic Graph the quadratic function y = 2x 2 + 4x – 3 Vertex is (-1, -5); axis of symmetry is x = Find two other points on the graph. xy = 2x 2 + 4x - 3(x, y) 0 (-1, -5) (0, -3) (1, 3) VERTEX from step 2 y = 2 (0) 2 +4(0) - 3 = -3 y = 2 (1) 2 +4(1) - 3 = Reflect points over axis of symmetry 4. Connect with a curved line.

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Aerial fireworks carry stars, which when ignited are projected into the air. Suppose a particular star is projected from an aerial firework at a starting height of 610 ft with an initial upward velocity of 88 ft/s. How long will it take for the star to reach its maximum height? How far above the ground will it be? The equation h = –16t t gives the height of the star h in feet at time t in seconds. Since the coefficient of t 2 is negative, the curve opens downward, and the vertex is the maximum point. Will the curve open down or up? (look at the coefficient of the t 2 ) Will the vertex be a max or min point? After 2.75 seconds, the star will be at its greatest height. b2ab2a – = –88 2(–16) = 2.75 h = –16(2.75) (2.75) + 610Substitute 2.75 for t. h = 731Simplify using a calculator. The maximum height of the star will be about 731 ft. Step 1. Find the x-coordinate of the vertex. Step 2: Find the h-coordinate of the vertex.

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