Assignment #2Nicole MostellerEMAT 6680

To make the new graph
for part one, I experimented with different values of **a**,
**b**, and **c**, in the basic equation for a parabola,
and then I decided that the easiest way to find the new graph
would be to use a bit of algebra and calculus to first find the
equation of the new parabola. To find the equation of a parabola
in the form

three points on the new graph are needed. Below is the explanation of how I found these three points as well as how I used these points to find arrive at the equation of the new graph.

Before finding the three points for the new graph, we need to manipulate the equation for the old graph that will make our work a bit easier. First simplify the equation

To find the vertex of the new graph, we can find the vertex of the new graph. From the work seen on Jadonna Brewton's Assignment #2 Write Up, we know that the vertex of a parabola can be found using the formula:

If , then the vertex is located at the point . Using this formula, the vertex for the original parabola which will be shared with the new parabola becomes . Substituting this point into the basic form for a parabola, we get our first equation .

The y-intercept of the
original graph is at the point **(0,16)**. To find the next
point on the new parabola, we know that the y distance from the
vertex of the old parabola to its y-intercept will be equal to
the y distance from the vertex to the y-intercept of the new parabola.
This equal distance is **21.125**. Now, to find the y-coordinate
of the y-intercept of the new parabola, let's take this distance,
**21.125** and add it to the y-distance of the vertex from
the x-axis, **5.125**.

The coordinate of the y-intercept for the new parabola is (0,-26.25). Substituting this point into the basic form for a parabola, we get our second equation-26.25 = c.

Because a parabola has a vertical line of symmetry
through the vertex, we can say that each point on one side of
a parabola has a "mate" on the opposite side of the
line symmetry. In the original parabola, the y-intercept's **(0,
16)**, symmetric "mate" is the point **(7.5, 16)**.
The symmetric mate for the y-intercept **(0, -26.25)**, of
the new parabola uses the same x coordinate.

The third point for the new parabola is (-7.5, -26.25). This point produces the third equation .

We now have the materials to build the equation of the new parabola. By solving this system of equations,

-26.25 = c

we find the solutions to be a = -2, b = 13, and c-26.25. The equation for the new parabola is .

Return to Previous Page | Return to Nicole's Page