COLLEGE BOARD Test 9 Math Section 3 #13

COLLEGE BOARD Test 9 Math Section 3 #13

Could you suggest a shortcut or fast way to solve this? All the answers are written in vertex form, so we can quickly eliminate two of them, as the coordinates of the vertex, as indicated by the graph provided, must be (3,1). That leaves choices A and C. Is there a quick way to solve from there without plugging in values from the graph?

Hello Mike, For problem 2 on page 284…

Hello Mike,
For problem 2 on page 284 (relating to “Working in Three Dimensions”), I had difficulty answering the question, because I don’t know what the inner radius of a sphere and how that differs from the outer radius of a sphere. Since I’m not able to find anything on the Internet that talks about this, could you please explain the difference to me?
And could you then tie it back to how the entire inner/outer radius thing is relevant to the question at hand (#2 on page 284)?

In question #10 of the backsolving chapter…

In question #10 of the backsolving chapter : in the xy plane, a line containing the points (a, a^3) and (10,40) passes through the origin. Which of the following could be the value of a?

I found the explanation in the answer key to be too time-consuming if I were to solve the equation with backsolving. Can you explain how to solve this question algebraically instead?