Which of the following equations represents the parabola shown in the xy-plane above?
Correct answer: C. y=2(x-3)2-8
- A. y = (x-3)2-8
- B. y = (x+3)2+8
- C. y=2(x-3)2-8
- D. y = 2(x+3)2 - 8
Explanation
Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y - mx - b)2 / (m2 +1) = (x - h)2 + (y - k)2.Using the vertex form of a parabola f(x) = a(x - h)2 + k where (h,k) is the vertex of the parabola.The axis of symmetry is x = 0 so h also equals 0.a = 1.Substituting the a value into the first equation of the linear systemIn mathematics, a parabola can be given in standard form, y = ax2 + bx + c, vertex form, y = a(x - h)2 + k where (h,k) is the vertex of the parabola, or intercept form, y = a(x - p)(x - q) where the x-intercepts of the parabola are at x = p and x = q.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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