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?

Sure thing. First, you’ve nailed it on vertex form. Because the vertex is (3, 1), you need to see . To differentiate between that leading coefficient being equal to 4 or 1, you need to remember what the leading coefficient tells you: how fast the parabola runs away from the vertex. Remember that your standard parabola looks like this:

Importantly, the first integer steps from the vertex are 1 across, 1 up. That’s what all parabolas with leading coefficient of 1 will look like.

Because the parabola in the question goes straight from vertex (3, 1) to (4, 5), it’s running away from the vertex faster than 1 across, 1 up. In fact, it’s going 1 across, 4 up, so we know its leading coefficient is 4 (it goes up 4 steps instead of 1).

But I wouldn’t even do that math. Once I saw that the parabola was running away from the vertex faster than the parabola, I’d know the answer isn’t C and go for A.

Does that help? Robin says: