Math 9 Lesson #39 – Graphing Quadratic Equations Mrs. Goodman

Quadratic Equation Highest degree = 2 Standard Form: y = ax 2 + bx + c Parabola: the graph of a quadratic equation (U- shaped)

y = x 2

y = -x 2

Characteristics of Parabola Parabola opens UP if a > 0 Parabola opens DOWN if a < 0 Parabola is wider if |a| < 1 Parabola is narrower if |a| > 1 c value is y-intercept

Vertex of Parabola x-coordinate of vertex = - b/2a y – coordinate of vertex: plug x-coordinate back into quadratic equation axis of symmetry is x-value of vertex

Example: y = 2x 2 – 8x + 4 a)Find vertex and axis of symmetry b)Graph parabola using the vertex and table of values

Example: y = 2x 2 – 8x + 4 a)Vertex: (2, -12) x = -b/2a = -(-8)/2(2) = 8/4 x = 2 y = 2(2) 2 – 8(2) + 4 y = -12

Example: y = 2x 2 – 8x + 4 b) Graph:

Try some more! Find the vertex, axis of symmetry, and graph each equation 1)2x 2 + 6x – 1 2)x 2 – 3x + 5

That’s all for today! Thanks for working hard! See you next time!