PSAT Math Multiple-Choice Question 773: Answer and Explanation

Question: 773

What is the x-coordinate of the minimum of the parabola with the equation y + 17= 6x² + 12x?

• A. -1
• B. 0
• C. 2
• D. 3

Correct Answer: A

Explanation:

(A) First, get the equation in standard form by subtracting 17 from both sides:
y = 6x² + 12x - 17
When a parabola is in standard form, y = ax² + bx + c, the axis of symmetry is given by the equation x = . Because the axis of symmetry passes through the vertex and this parabola opens up, the x-value that gives the axis of symmetry will also give the x-coordinate of the vertex. The y- and x-values of the vertex give the minimum value and its location on the parabola, respectively, so we want to know the x-value of the vertex to solve this problem.
In this case, a = 6 and b = 12, so:

This corresponds to choice (A).
Alternatively, you could have converted the equation to vertex form by completing the square to get:
y = 6(x + 1)2 - 23.
Then the vertex is (-1, -23), so x = -1.