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**HallsofIvy** Any thing done **before** the "main function" changes x (and so affects the graph horizontally), anything done **after** the "main function" changes y (and so affects the graph vertically).

Here your "main function" is given as $\displaystyle y= x^2- 1$. $\displaystyle 5x^2- 5= 5(x^2- 1)$ multiplies by 5 **after** doing $\displaystyle x^2- 1$ and so affects the graph vertically.

The x-intercepts are where the graph "intercepts" the x-axis and so y= 0. $\displaystyle y= 4x^2- 1= 0$ is the same as $\displaystyle 4x^2= 1$ or $\displaystyle x^2= \frac{1}{4}$. The x-intercepts are at x= $\displaystyle \frac{1}{2}$ and $\displaystyle x= -\frac{1}{2}$. Some people refer to the "x-intercepts" as just the x value ($\displaystyle \frac{1}{2}$ and $\displaystyle -\frac{1}{2}$) and some as the **points** ($\displaystyle \left(\frac{1}{2}, 0\right)$ and $\displaystyle \left(-\frac{1}{2}, 0\right)$. Check with your teacher or textbook to see which convention is used in your class.

The y-intercepts are where the graph "intercepts" the y-axis and so x= 0. Just put x= 0 into $\displaystyle y= 4x^2- 1$ to get y= -1. Again, the y-intercept is either the value y= -1 or the point (0, -1) depending on the convention used.

I have no idea what "math pure 30" is but (liberal arts) colleges want you to be educated in a broad range of subjects. You will very likely be required to take at least one mathematics course in college.