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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