Final answer:
The zeros of the function f(x) = -(2x - 3)^2 + 25 are x = 4 and x = -1, and the vertex of the parabola is (3/2, 25).
Step-by-step explanation:
To find the zeros of the function f(x) = -(2x - 3)2 + 25, we set the function equal to zero and solve for x. The equation becomes -(2x - 3)2 + 25 = 0. This simplifies to (2x - 3)2 = 25. Taking the square root of both sides gives two solutions, 2x - 3 = ±5. Solving for x yields the zeros x = 4 and x = -1.
To find the vertex of the parabola, we look at the equation in vertex form, which is already given: f(x) = -(2x - 3)2 + 25. The vertex of the parabola in this form is the point (h, k), where h is the x-value that makes the square term zero, and k is the constant term. Hence, the vertex is (3/2, 25).