9.1 Graphing Quadratic Functions Quadratic Function: in the form of… y = ax2 + bx + c, where a = 0. The graph of a quadratic function is a parabola (generally looks like a U). Algebra 1

Parabolas can open up or down. Maximum Vertex Parabolas can open up or down. The point where the curve changes direction is called the vertex. The highest point is called a maximum. This only happens if the parabola opens down. The lowest point is called a minimum. This only happens if the parabola open up. a < 0 a > 0 Minimum Vertex

Graph a quadratic function y = x2 – x – 2 a > 0: Smile Minimum at the vertex. Step 1: Pick 5 values for x to plug in. Step 2: Plug values in for x and then plot them on the graph…connect all the dots. -2 (-2)2 – (-2) - 2 (-2, 4) = 4 + 2 – 2 = 4 (-2, 4) -1 (-1)2 – (-1) - 2 (-1, 0) (2, 0) = 1 + 1 – 2 = 0 (0)2 – (0) - 2 (-1, 0) (0, -2) = 0 - 0 – 2 = -2 (0, -2) (1, -2) 1 (1)2 – (1) - 2 = 1 – 1 – 2 = -2 (1, -2) 2 (2)2 – (2) - 2 = 4 – 2 – 2 = 0 (2, 0)

Each parabola has an axis of symmetry Each parabola has an axis of symmetry. This is where you could “fold” the parabola in half and the sides would match up (symmetrical). The axis goes through the vertex. The equation for finding the axis of symmetry is… given a quadratic function

Graph y = -2x2 – 8x - 2 Write the equation of the axis of symmetry Is the vertex a maximum or a minimum? A smile or frown? Graph y = -2x2 – 8x - 2 a < 0: Frown! Maximum! Write the equation of the axis of symmetry a = -2, b = -8, c = -2 Find the coordinates of the vertex. The x-value is the same as the axis of symmetry. Plug that number (-2) into the equation to get the y-value. vertex (-2,6) y = -2x2 – 8x – 2 y = -2(-2)2 – 8(-2) – 2 y = -2(4) + 16 – 2 y = -8 + 16 – 2 y = 6 Vertex: (-2,6)

y = -2x2 – 8x - 2 Pick 2 values to the right of the axis of symmetry. Let x = -1 Let x = 0 Plug them into the original function to get your y-values. vertex (-2,6) y = -2x2 – 8x – 2 y = -2(-1)2 – 8(-1) – 2 y = -2(1) + 8 – 2 y = -2 + 8 – 2 y = 4 (-1,4) y = -2x2 – 8x – 2 y = -2(0)2 – 8(0) – 2 y = -2(0) + 0 – 2 y = 0 + 0 – 2 y = -2 (0,-2) (-1,4) (0,-2) Reflect the points over the axis of symmetry. Connect the dots with a smooth curve.