SAT Math · Equivalent expressions · medium
What is the maximum value of the function f(x) = -x² + 10x - 21?
What is the maximum value of the function ?
Answer and explanation
Answer: A: 4
Complete the square: . Because of the negative sign, the parabola opens downward and its highest point is the vertex . The maximum value is 4, choice A. Check by plugging in: . Choice B () is the -intercept. Choice C (5) is where the maximum occurs, the -coordinate. Choice D (10) is the -coefficient. The maximum value is the output, not the input.
More Equivalent expressions questions
- Question 9 · mediumThe function f(x) = x² - 8x + 19 is equivalent to which of the following, where the minimum value…
- Question 16 · easyIf (x+3)(x-5) = x² + bx + c for all values of x, what is the value of b?
- Question 32 · easyFor x ≠ 4, which expression is equivalent to (x² - 16)/(x - 4)?
- Question 61 · hardLet u = x² - 1. If u² - 7u + 10 = 0, how many distinct real values of x satisfy this equation?
- Question 62 · mediumIf x + y = 7 and xy = 10, what is the value of x² + y²?
- Question 74 · mediumIn the expansion of (x+5)(2x-3), what is the coefficient of the x term?
Learn the method behind questions like this one
The SAT Math course teaches each tested skill through lessons, step-by-step solutions to sample problems, the complete study guide and full-length practice tests.