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

2. 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 Graphing Quadratic Equations Using Vertex form Vertex:

3. 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. Graphing Quadratic Equations Using Vertex form Graphing Quadratic Equations Using Vertex form

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

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