My Parabola

Above is a graph of my parabola, shown in red, compared to the parent function of a parabola in blue.

The general form of an equation is as follows:

This equation provides a few more variables in comparison to the parent function form. Those variables being a, h, and k.

The a in the equation denotes the width of the parabola, as in how wide the parabola stretches or compresses. A parent function grows in an exponential rate, and the a in the equation is the coefficient that controls the rate in which the parabola expands. If the coefficient was to be 2, the parabola would be twice as compressed, as the rate would increase twice as much. If we were to make the coefficient 1/4, which is the case in my parabola equation, the parabola would be four times as stretched, as the rate would decrease four times as much. Additionally, the a coefficient also dictates which way the parabola opens. If the coefficient was negative, the parabola would open downwards, meaning the vertex would have the greatest y value. If the coefficient was positive, which is the case for my parabola, it would open upwards, meaning the vertex would have the smallest y value.

The h in the equation denotes how far out the vertex begins on the x-axis. In a parent function, the vertex starts at x = 0. In my parabola, the h value is -5, meaning that the vertex would start 5 spaces to the left. The reason as to why the parabola places on the left side, even though our h value appears positive is because on the x-axis, the y-intercept would be equal to zero. The value of x that we would need must make the equation equal to zero. In my parabola, since the x value is +5, h would then need to equal the amount that would cancel it out, which in this case would be -5.

The k in the equation denotes how far out the vertex begins on the y-axis. In a parent function, the vertex starts at y = 0. In my parabola, the k value is -7, meaning that the vertex would start 7 spaces below the x-axis.

Self – Assessment

I demonstrated the same mathematical idea in multiple ways by comparing my parabola to the parent function repeatedly. Within each explanation to different variables, I would explain how the variables effect the parent function, and how mu equation differs from it.
I used relevant vocabulary to make my explanations easier to follow. I used words such as vertex, variable, function, x-intercept, and y-intercept.
In order to organize my writing, I would bold key words that make it easier to follow and read. I also displayed the general form of the equation to better relate my explanations to the equation, and to the parent function.