Recall Evaluate an Expression 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 Objectives: Graph quadratic functions Recall Evaluate an Expression –b 2a Evaluate the expression for a = –6 and b = 4. –b 2a –4 2(-6) –4 -12 1 3 = = = Recall Role of 'a' and 'c' Form of a Quadratic Equation: ax2 + bx + c Coefficient (a) affects the width of the parabola Constant (c) affects the movement up or down

Role of ‘b’ in a Quadratic Function 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 =

Explore the Role of ‘b’ when Graphing a Quadratic Graph the quadratic function y = 2x2 + 4x – 3. Find the equation of the axis of symmetry. Substitute values into x = Find the coordinates of the vertex using the x value. Substitute x = -1 into the equation to find corresponding y value y = 2x2 + 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 = 2x2 + 4x – 3 Vertex is (-1, -5); axis of symmetry is x = -1 3. Find two other points on the graph. x y = 2x2 + 4x - 3 (x, y) -1 VERTEX from step 2 (-1, -5) y = 2 (0)2 +4(0) - 3 = -3 (0, -3) y = 2 (1)2 +4(1) - 3 = 3 1 (1, 3) 3. Reflect points over axis of symmetry 4. Connect with a curved line.

Will the curve open down or up? (look at the coefficient of the t2) 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 = –16t2 + 88t + 610 gives the height of the star h in feet at time t in seconds. Will the curve open down or up? (look at the coefficient of the t2) Will the vertex be a max or min point? Since the coefficient of t 2 is negative, the curve opens downward, and the vertex is the maximum point. Step 1. Find the x-coordinate of the vertex. b 2a – = –88 2(–16) 2.75 After 2.75 seconds, the star will be at its greatest height. Step 2: Find the h-coordinate of the vertex. h = –16(2.75)2 + 88(2.75) + 610 Substitute 2.75 for t. h = 731 Simplify using a calculator. The maximum height of the star will be about 731 ft.