# Graphing from Vertex Form

### By: Jaspreet Saini

## 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?

## Answers

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