Foundations

Graphing a Quadratic

Example

Graph the quadratic equation y = 2x2 ? 8x + 6.

Step 1. Determine a, b and c and decide if the graph will open up or down.

a = 2, b= -8, and c = 6. Because a is positive, the graph will open upward.

Step 2. Find the vertex.

GraphQuadEx1-1

The vertex is at the point (2, -2)

Step 3. Find the x-intercepts.

To find the x-intercepts, substitute 0 in for the y and solve. This was covered completely in the solving book.

2x2 ? 8x + 6 = 0

2(x2 - 4x +3) = 0

2(x - 1)(x -3) = 0

x = 1 or x = 3

The x-intercepts are (1,0) and (3,0).