Presentation on theme: "Recall Evaluate an Expression"— Presentation transcript:
1Recall 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 representationObjectives:Graph quadratic functionsRecall Evaluate an Expression–b2aEvaluate the expression for a = –6 and b = 4.–b2a–42(-6)–4-1213===Recall Role of 'a' and 'c'Form of a Quadratic Equation: ax2 + bx + cCoefficient (a) affects the width of the parabolaConstant (c) affects the movement up or down
2Role of ‘b’ in a Quadratic Function Coefficient (b) affects the position of axis of symmetryvertex moves right or leftaxis of symmetry changesequation of axis of symmetry is x =
3Explore 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 valuey = 2x2 + 4x – 3.= 2(-1)2 + 4(-1) – 3= 2 – 4 – 3= -5Coordinates of the vertex is (-1, -5)
4Explore the Role of ‘b’ when Graphing a Quadratic Graph the quadratic function y = 2x2 + 4x – 3Vertex is (-1, -5); axis of symmetry is x = -13. Find two other points on the graph.xy = 2x2 + 4x - 3(x, y)-1VERTEX from step 2(-1, -5)y = 2 (0)2 +4(0) - 3= -3(0, -3)y = 2 (1)2 +4(1) - 3= 31(1, 3)3. Reflect points over axis of symmetry4. Connect with a curved line.
5Will 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 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.b2a–=–882(–16)2.75After 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) Substitute 2.75 for t.h = Simplify using a calculator.The maximum height of the star will be about 731 ft.