Presentation on theme: "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."— Presentation transcript:
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
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
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)
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.
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.