Quadratic Functions

Learn to graph parabolas using the vertex form!

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.

Frequently asked questions

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

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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

Quadratic Word problems typically ask for the following information:

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