Question

The graph of a parabola in the xy-plane has the following characteristics. It opens downward, It has a z-intercept at the point (5,0). Its vertex is at the point (2,18). Which of the following is the equation of the parabola?

A) y= -2(x+1)(x-5)
B) y= -(x-1)(x-5)
C) y = - (18/21) (x - 5)(x + 5)
D) y = (18/7) (x - 1)(x + 5)

Answer 1

The equation of the parabola with the given characteristics is y = -2(x-2)^2 + 18, which matches the given equation A) y = -2(x+1)(x-5).

Step-by-step explanation:

The equation of the parabola with the given characteristics is y = a(x-h)^2 + k, where (h,k) represents the vertex. Since the parabola opens downward, the coefficient 'a' should be negative. The z-intercept is the point where the parabola intersects the x-axis, which means y = 0 at that point. Therefore, substituting the values (5,0) and (2,18) into the equation, we can solve for 'a' to find the equation of the parabola.

18 = a(2-5)^2 + 18
0 = a(5-5)^2 + 18
Solving these equations, we find that a = -2. Substituting this value back into the equation, we get y = -2(x-2)^2 + 18, which matches the given equation A) y = -2(x+1)(x-5).