PSAT Math Grid-Ins Question 44: Answer and Explanation

Question: 44

If the equation of the parabola shown in the graph is written in standard quadratic form, y = ax² + bx + c,and a = -1, then what is the value of b ?

Correct Answer: 6

Explanation:

6

Difficulty: Hard

Category: Passport to Advanced Math/Quadratics

Getting to the Answer: When you are given the graph of a parabola, try to use what you know about intercepts, the vertex, and the axis of symmetry to answer the question. Here, you could try to use points from the graph to find its equation, but this is not necessary because the question only asks for the value of b. As a shortcut, recall that you can find the vertex of a parabola using the formula (the quadratic formula without the radical part). You are given that a = -1. Now, look at the graph—the vertex of the parabola is (3, 8), so substitute 3 for x, -1 for a, and solve for b:

As an alternate method, you could plug the value of a and the vertex (from the graph) into vertex form of a quadratic equation and simplify:

The coefficient of x is b, so b = 6.