# Graphing from Vertex Form

## Summary

The vertex form of a parabola is y=a(x-h)² + k. The a value affects the direction in which the parabola is opening and whether the parabola is vertically stretched or compressed. If -1< a <1 the parabola would be vertically compressed and if a> 1 or a <-1 the parabola would be vertically stretched. The h value affects the horizontal translation. If h >0 the vertex moves to the right and if h <0 the vertex moves to the left by h units. The k value affects the vertical translation. If k >0 the vertex moves up and if k <0 the vertex moves down by k units.

## Graphing using Vertex Form

Plot the vertex using the h and k values. Using the a value determine the different y values by substituting possible values of x.

## Try this word problem

A soccer ball is kicked into the air. It's height in meters after t seconds is given by

h= -4.9 (t-2.4)² +29.

a) What was the height of the soccer ball when it was kicked?

b) How high was the ball after 2 seconds?

a) t=0

h= -4.9 (0-2.4)² +29

=0.776 (round) = 0.77

Therefore, the soccer ball was 0.77m off the ground.

b) t represents time so plug in 2

h= -4.9(2-2.4)² +29

= 28.2

Therefore, the ball was 28.2m high after 2 seconds.

Math video