Algebra I Recipe: Graphing a Quadratic Equation

A. Definitions

1. Parabola – the graph of a quadratic function, which is u-shaped
2. Vertex Point – it’s the highest or lowest point on the graph
3. Axis of Symmetry – the vertical line that goes through the vertex point
4. Standard Form - y = ax² + bx + c

B. Steps for Graphing a Quadratic Equation in Standard Form

1. Determine if the graph will open up or down.
• Opens up if "a" is positive.
  The vertex point will be the minimum point.
• Opens down if "a" is negative.
  The vertex point is the maximum point.
2. Find the vertex point.
• Find the x-value by x = - b/(2a).
• Find the y-value by substituting the x-value into the equation and solving for "y".
3. Find more points to determine the graph.
• Choose two integers larger than the x-value of the vertex point.
• Choose two integers smaller than the x-value of the vertex point.
• Substitute these values in place of "x" in the equation and solve for "y".
• Four ordered pairs have been found
4. Graph and connect all points that have been found.

Practice Problems