By: Melissa Wilson

In this assignment we will investigate values for

ain:We will look at various values for

a: -5, -3, -1, 1, 3, 5First let's look at the difference between positive and negative coefficients. All of the equations with positive coefficients open upward (concave up) and the negative coefficients all point downward (concave down). Since the x-term is squared, for any value of x, that term is positive. Therefore, the coefficient solely determines the sign for the y value. Hence, the positive

avalues will give all positive values for y and and negativeavalues will make all the y values negative.Now, look at the difference in the coefficients based on their scale. As the absolute value of the

acoefficient increases the width of the parabola gets smaller. This is because as theaincreases, the corresponding y-value increases. For instance, let's compare the value atx=2for two separate equations. First,Now, for another,

We can easily see that a coefficient of 3 will increase the y-value at a given x by 3 times. Hence, the y-values for the parabola will increase more rapidly as the absolute value of a increases.

Below you will see an animation of with n varying from -10 to 10.