Graphing Quadratic Equations CA 21.0, 23.0

Objective - To graph a quadratic equation

Write the answer as an ordered pair Graphing Quadratics Step 1: Find the axis of symmetry Step 2: Find the vertex Plug your answer from step 1 into the original equation and solve for y Write the answer as an ordered pair (x,y) Step 3: Find the y-intercept Identify c (0,c)

Graphing Quadratics Step 4: Make a T-Chart that includes the vertex as the middle point and the y-intercept Step 5: Plot the points on the graph x y = f(x) = ax2+bx+c y

GRAPH : y = x2 – 4x – 5 a = 1, b = – 4, c = –5 The vertex: y = x2 – 4x – 5 y = (2)2 – 4(2) – 5 y = 4 – 8 – 5 y = – 9 (2, – 9) c = –5 (0, –5)

T-Chart x y = f(x) = x2 – 4x – 5 y –5 2 y = (2)2 – 4(2) – 5 –9

The Graph

GRAPH : y + 6x = x2 + 9 y = x2 – 6x + 9 a = 1, b = – 6, c = 9 The vertex: y = x2 – 6x + 9 y = (3)2 – 6(3) + 9 y = 9 – 18 + 9 y = 0 (3, 0) c = 9 (0, 9)

T-Chart x y = f(x) = x2 – 6x + 9 y 9 3 y = (3)2 – 6(3) + 9

The Graph