# Graphing Vertex Form

## What have we learned this unit?

Over the last two weeks, we have learned:

1. How to determine whether a relation is Linear, Quadratic, or Neither.

2. How to graph the quadratic equation y = a(x-h)² + k using a point and the vertex.

3. How transformations of a parabola affect it's equation.

## Another way we can showcase our understanding, is through word problems.

Here's an example:

A person who is 2m tall throws a ball from the top of his head. It reaches a maximum height of 14m after 3 seconds.

What is the equation? Analyzing the word problem, we can extract both the Vertex, and the Y-Intercept.

Vertex: (3,14) - Peak height of the ball

Y-Intercept: (0,2) - How high the ball is at 0 seconds

Now that we have our two points, we can plug them into Vertex form.

Y=a(x-h)²+k

= y=a(x-3)²+14 (Vertex plugged in)

= 2 = a(0-3)²+14 (Y-Intercept plugged in)

= 2-14 =a(0-3)²+14-14

=-12 = a(0-3)²

=-12 = a(-3)²

=-12/9 = 9a/9

= -1.33 = a

Now that we have our A value, we have the entire equation, which is

y = -1.33(x-3)²+14

and on a graph, it looks like this

## Finally, the last thing we learned was how transformations affect a parabola and its equation.

How Transformations affect the Vertex Form of a Parabola