The key to this question: Do you see the number that comes right before the [tex] x^{2} [/tex] term?
If that number has a negative sign before it, it is negative and the graph will point downwards. However, if it is a positive number, the graph will point downwards.
You can now eliminate options 2 and 4, because they are negative and you want a graph that is positive.
Now look at how large that integer is. Ignore the negative sign completely if there is one. The larger it is, the narrower your graph will be. Imagine the slope of a normal line. If the slope is a larger number, it will be more steep and therefore more narrow.
An equation is quite literally altering the x value to get a y value. If x = y, for every x value you have, y will be exactly the same. However, if you multiply x by a number, like [tex] \frac{1}4}[/tex] or 5, the y value will then become smaller or bigger. When this happens, the graph becomes wider or narrower. When that integer is larger, the graph will become narrower.
Now take your equation y = −3x^2 + 2x − 1.
Because you want a graph that is narrow, find an integer that is larger than 3.
The only option with an integer that is larger than 3 and is positive is Option 1.
The answer is Option 1, y = 4x2 − 2x − 1
