Final answer:
The function g(x)=−5(1–3)^2 does not have an x-intercept, as it represents a horizontal line at y = −5. The vertex of the function is (3, −5), which is the point where the parabola would assume its maximum or minimum value.
The correct option is not given.
Step-by-step explanation:
To find the x-intercept and vertex of the quadratic function g(x)=‑5(1‑3)^2, we must understand the structure of the function and what these terms represent. The general form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola, and the x-intercept is the value of x for which g(x) = 0.
Looking at the given function, g(x)=‑5(1‑3)^2, we see that it's already in vertex form with h = 3 and k = 0 (since the function equals zero). Therefore, the vertex of the function is (3, 0). However, since the function g(x) does not contain an x that we can solve for g(x) = 0, there is no x-intercept. Our function is a constant, which means it represents a horizontal line at y = ‑5, not touching the x-axis at all.
The correct options for the function's x-intercept and vertex would thus be none for x-intercept, since it does not cross the x-axis, and (3, ‑5) for the vertex, considering the shape of the quadratic function described.
The correct option is not given.