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