# Graphing Vertex Form

### By: Corey Vongphakdy

## What have we learned this unit?

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.

## At first, we learned about the basics of quadratics, and what makes an equation quadratic; when a variable becomes squared. We also learned about first and second differences, and how to tell if a relation is Linear or Quadratic. | ## And then, we learned about the main character of the unit: The Parabola. We discussed the many parts of the Parabola, including the Axis of Symmetry, Vertex, Y and X intercepts, and so on. At first, I was hard pressed to see where a Parabola would occur in real life, but as we did word problems, it became clear. Parabolas are part of our everyday lives. Just recently, I used them to calculate bike hills and trails. | ## Finally, we learned the Vertex Form of a Parabola, y = a(x-h)²+K, and how the position of the Parabola directly affects this equation, and what each variable represents on the graph. We also learned how different types of transformations affect different variables of the equation, and to what extent. |

## At first,

We also learned about first and second differences, and how to tell if a relation is Linear or Quadratic.

## And then,

At first, I was hard pressed to see where a Parabola would occur in real life, but as we did word problems, it became clear. Parabolas are part of our everyday lives. Just recently, I used them to calculate bike hills and trails.

## Finally,

We also learned how different types of transformations affect different variables of the equation, and to what extent.

## So when we put everything we learned together, here's what it looks like on a Graph

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

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