SAT Math · Nonlinear functions · easy

A parabola has zeros at x=-2 and x=8. What is the x-coordinate of the vertex of the parabola?

A parabola has zeros at x=−2x=-2 and x=8x=8. What is the xx-coordinate of the vertex of the parabola?

Answer and explanation

Answer: D: 3

A parabola is symmetric about its axis, which passes through the vertex. The axis is exactly halfway between the two zeros, so the vertex's xx-coordinate is the average of −2-2 and 88: −2+82=3\frac{-2 + 8}{2} = 3, choice D. Choice A (6) is the sum of the zeros. Choice B (5) is half the distance between the zeros, 8−(−2)2\frac{8-(-2)}{2}, which gives the half-width of the parabola, not the position of its center. Choice C (−5-5) comes from a sign error with that half-distance. Add the zeros and divide by 2.

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