- The parabola in the figure above has its minimum at
x= 2. Which of the following could be anx-intercept of the parabola?

(A) 2.5

(B) 3

(C) 3.5

(D) 4

(E) 4.5

Answer and explanation after the jump…

The most important thing you can remember about parabolas is this: * A PARABOLA IS ALWAYS SYMMETRICAL*. Once you know the line of symmetry (in our case here, it’s

*x*= 2), you’re usually good to go.

Note that the leftmost *x*-intercept is negative. This is super-important. It means that the distance from the line of symmetry to the parabola when *y* = 0 is GREATER THAN 2!

Think about it: if the line of symmetry is at *x* = 2, and the left *x*-intercept is negative, then the distance from the line of symmetry to that *x*-intercept HAS to be greater than 2. If it wasn’t, the intercept wouldn’t be negative! What this means is that the distance from the line of symmetry to the *x*-intercept on the right has to be greater than 2 as well!

The only answer choice that gives us a point further than 2 units away from the line of symmetry for our *x*-intercept on the right is choice (E), 4.5. That’s gotta be our answer.

## Comments (2)

That is what I guessed b/f scrolling down. In fact, I believe I was using my newfound guestimating skills.

Argh! Had to read it about 10 times before I got it – but now I get it. Woot!