Graphing Quadratic Equations

1. Graphing Quadratic Equations Vertex Form of a Quadratic Function: A quadratic function with vertex at (h, k) can be written as: Using Vertex form

2. Graphing Quadratic Equations • Using Vertex form Vertex: • The “a” in the formula has the same properties as the “a” in the formula for standard form. • (a is positive), then the U-shape opens up. • (a is negative), then the -shape opens down. • “big” |a|  narrow graph • “small” |a|  wide graph

3. Graphing Quadratic Equations Graphing Quadratic Equations • Using Vertex form • Using Vertex form • To graph: • Plot the vertex (h, k) {be careful of the sign of the h-value} • Use the value of “a” to determine whether the graph opens up or down. {positive “a”  up, negative “a”  down} • Use the value of “a” to determine the width of the graph. • Think of “a” as the “initial slope” of the curve. • If a = 1, then move from the vertex up 1 and right 1 to find another point on the graph. • If a = 2, then move from the vertex up 2 and right 1 to find another point on the graph. • If a = -2, then move from the vertex down 2 and right 1 to find another point on the graph • Etc. • Use the line of symmetry as a guide to draw a smooth U-shaped curve.

4. Graphing Quadratic Equations • Using Vertex form Example:Sketch the graph of Line of Symmetry Vertex Positivea U-shape opens up up 1and right 1 from the vertex

5. Graphing Quadratic Equations • Using Vertex form Example:Sketch the graph of Line of Symmetry Vertex negativea U-shape opens down down 2and right 1 from the vertex