## Learning Goals

• Learn to graph using the vertex form equation, which is y=a(x-h)+k
• Learning how to use a table of values to create parabolas
• Learn how to graph transformations of the parabolas and mapping notation

## The unit in summary

We will be using the vertex form "y=a(x-h)+k to move, translate, and form a parabola.

Is this the only way to model parabolas?

• No, there are two others but they will not be covered right now
Will the y-intercept always be the vertex of the parabola?

• No, the y-intercept can any point in which the parabola crosses the y- intercept

## Graphing parabolas

This picture is an example of graphing parabolas. The parabola in the middle of the grid is a basic parabola. The equation for a basic parabola is y=x^2. The Parabola in the bottom right corner of the grid is a new parabola that has been transformed. The equation for the new parabola is y=-3(x-8)^2-4. In order to find the points for the new parabola, you must plug the vertex form into the table of points that form the basic parabola.

## Solving quadratic equations with word problems

1. What is the maximum height of the ball?

Ans. Find the vertex, the y-value is the maximum height y=k

2. At what time did the ball reach the maximum height?

Ans. Find the vertex, the x-value is the time when the max height occurred x=h

3. What was the initial height of the ball?

Ans. Set x=0 and solve for y or Find the y-intercept

4. How long was the ball in the air?

Ans. Set y=0 and solve for x or Find the x-intercept

5. When did the ball hit the ground?

Ans. Same as previous question

7. What is the height of the ball at 3 seconds?

Ans. Sub the x-value into the equation to solve for y.sub t into the equation to solve for h.

(t=x, h=y, basically x and t represent the same thing, which is time and h reps the same thing as y, which is height.)

Information provided by Ms.Dhaliwal