1. 5.1 – Modeling Data with Quadratic Functions

2. QUADRATICS - - what are they? Important Details o c is y-intercept o a determines shape and position if a > 0, then opens up if a < 0, then opens down o Vertex: x-coordinate is at –b/2a FORM _______________________ Y = ax² + bx + c Quadratic term Linear term Constant

3. Parts of a parabola This is the y-intercept, c It is where the parabola crosses the y-axis This is the vertex, V This is the called the axis of symmetry, a.o.s. Here a.o.s. is the line x = 2 These are the roots Roots are also called: -zeros -solutions - x-intercepts

4. STEPS FOR GRAPHING Y = ax² + bx +c 1HAPPY or SAD ? 2VERTEX = ( -b / 2a, f(-b / 2a) ) 3T- Chart 4Axis of Symmetry

5. GRAPHING - - Standard Form (y = ax² + bx + c) y = x² + 6x + 8 1) It is happy because a>0 2) FIND VERTEX (-b/2a) a =1 b=6c=8 So x = -6 / 2(1) = -3 Then y = (-3)² + 6(-3) + 8 = -1 So V = (-3, -1) 3) T-CHART X Y = x² + 6x + 8 -2 y = (-2)² + 6(-2) + 8 = 0 0 y = (0)² + 6(0) + 8 = 8 Why -2 and 0? Pick x values where the graph will cross an axiw The graph will be symmetric al. Once you have half the graph, the other two points come from the mirror of the first set of points.

6. GRAPHING - - Standard Form (y = ax² + bx + c) y = -x² + 4x - 5 1) It is sad because a<0 2) FIND VERTEX (-b/2a) a =-1 b=4c=-5 So x = - 4 / 2(-1) = 2 Then y = -(2)² + 4(2) – 5 = -1 So V = (2, -1) 3) T-CHART X Y = -x² + 4x - 5 1y = -(1)² + 4(1) - 5 = -2 0y = -(0)² + 4(0) – 5 = -5 Here we only have one point where the graph will cross an axis. Choose one other point (preferably between the vertex and the intersection point) to graph.