Graphing Quadratic Equations Section 9.4 Graphing Quadratic Equations

Example Graph the equation y = x2 by plotting points. y x y x 2 4 1 3 4 1 2 3 4 y x 2 4 1 1 1 1 2 4 2

Example Graph the equation y = x2 by plotting points. y x y x 2 4 1 2 3 4 1 2 3 4 y x 2 4 1 1 1 1 2 4 3

Graphs of Quadratic Equations The graph of the quadratic equation y = ax2 + bx + c is a parabola. The vertex is the lowest point on a parabola that opens upward or the highest point on a parabola that opens downward. x y 1 2 3 4 1 2 3 4 vertex vertex 4

Vertex of a Parabola Vertex of a Parabola The x-coordinate of the vertex of the parabola described by y = ax2 + bx + c is 5

Example Determine the vertex of y = 3x2 + 6x – 7. y = 3x2 + 6x – 7 = 3(1)2 + 6(1)  7 = 3  6  7 (1, ?) = 10 The vertex is (–1, –10). 6

Example Determine the vertex and x-intercepts of y = –2x2 – 8x + 4 and sketch the graph. y = –2x2 – 8x + 4 = –2(2)2 – 8(2) + 4 = –2(4) + 16 + 4 = 12 The vertex is (–2, 12). Continued 7

Example (cont) Determine the vertex and x-intercepts of y = –2x2 – 8x + 4 and sketch the graph. The x-intercepts occur where y = 0. x y 2 4 6 8 2 4 6 8 12 16 12 16 –2x2 – 8x + 4 = 0 vertex Use the quadratic formula to determine the x-intercepts. x = 4.4 x = 0.4 8