SAT Math Multiple Choice Question 574: Answer and Explanation
The following quadratic equations are all representations of the graph shown above. Which equation could you use to find the minimum value of the function, without doing any additional work?
Correct Answer: A
Category: Passport to Advanced Math / Quadratics
Strategic Advice: Quadratic equations can be written in several different forms, each of which reveals something special about the graph. For example, factored form reveals the solutions, or x-intercepts, of the graph, while standard form reveals the y-intercept.
Getting to the Answer: The minimum value of a quadratic function is equal to the y-value of the vertex of its graph, so vertex form, y = a(x – h)2 + k, reveals the minimum without doing any additional work. Choice (A) is the only equation written in this form and therefore must be correct. The minimum value of this function is .