Objective: To us the vertex form of a quadratic equation 5-3 TRANSFORMING PARABOLAS

In the following table the first column is written in standard form. In the second column, each function has been written in vertex form. Use multiplication to verify that the functions in each row are equivalent. Compare the values ofandin each row. Write a formula to show the relationship betweenand

Standard form :Vertex Form :

THE FAMILY OF QUADRATIC FUNCTIONS Vertical Stretch or Shrink, and/or Reflection in the x-axis Parent Function: Reflection in x-axis: Stretch (a>1) or shrink (0<a<1) by factor a: Reflection in x-axis: Vertex Form The graph (and vertex) ofshifts h units horizontally and k units vertically. For h>0, the graph shifts right. For h<0, the graph shifts left. For k>0, the graph shifts up. For k<0, the graph shifts down. The vertex is (h, k) and the axis of symmetry is the line x = h.

USING VERTEX FORM TO GRAPH A PARABOLA Graph STEP 1: Identify the vertex ( h, k ) --Graph the vertex and draw the axis of symmetry STEP 2: Find another point. (Pick a value for x and put into the equation to find y) Step 3: Use the fact that parabolas are symmetric to plot second point Step 4: Sketch the curve

Write the equation of the parabola using vertex form. Substitute (5, -4) into this equation to find a The equation of the parabola is

Use vertex form to write the equation of the parabola