I’m having a problem with Problem 6 from the 00 Prereq webwork problems. The problem gives me the following graph:
The problem states that the graph is "obtained from that of f(x)=x^2 by a combination of scaling and shifting. It then asks me for a formula for the graph. I can sort of see that it’s going to involve a -(x-1)^2 and a +4 but I can’t quite seem to get it. Any help would be appreciated!
You’re so close! The general form is going to be
That’s what it means to say that it’s formed from a combination of stretching and shifting.
Now you’re absolutely right that b=1 and c=4. I guess that a will be negative, since the parabola is upside down. To see exactly what the value of a is, use the fact that the y-intercept is 1. Since the y-intercept occurs when x=0, that yields an algebraic equation:
which means that a=-3. Thus our formula is
You can check it on Desmos.