NO LINKS!!! 4. Sam was kicking a soccer ball and she noticed that the path of the ball was a parabola. The highest point the ball reached was 28 feet and the ball landed 20 feet away from where she was standing.

5. Rasheed was playing kickball when he noticed that the path of the ball was a parabola. The highest point the ball reached was 12 feet and the ball landed 100 feet from where he was standing.

Refer to this previous solution set

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Problem 4

Like the three earlier problems, we'll place the kicker at the origin and have her kick to the right. The two roots in this case are x = 0 and x = 20 to represent when the ball is on the ground.

This leads to the factors x and x-20 and the equation

We'll plug in (x,y) = (10,28) which is the vertex point. The 10 is the midpoint of 0 and 20 mentioned earlier.

Let's solve for 'a'.

This then leads us to:

The equation is in the form with

The graph is below in blue.

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Problem 5

The same set up applies as before.

This time we have the roots x = 0 and x = 100 to lead to the factors x and x-100. We have the equation

We'll use the vertex point (50,12) to find 'a'.

Then we can find the standard form

The graph is below in red.