To determine the coordinates of the vertex of the given parabola equation, let's first recognize that the equation is in the vertex form of a parabola. The vertex form of a parabolic equation is given by:
[tex]\[ y = a(x - h)^2 + k \][/tex]
where [tex]\((h, k)\)[/tex] represents the coordinates of the vertex of the parabola.
Given the specific equation:
[tex]\[ y = -4(x - 3)^2 + 5 \][/tex]
we can identify the values of [tex]\(h\)[/tex] and [tex]\(k\)[/tex] directly from the equation.
- The term inside the squared parentheses, [tex]\( (x - 3) \)[/tex], tells us that [tex]\(h = 3\)[/tex].
- The constant term outside the squared expression, [tex]\( + 5 \)[/tex], tells us that [tex]\(k = 5\)[/tex].
Hence, the coordinates of the vertex are [tex]\((h, k) = (3, 5)\)[/tex].
Therefore, the correct answer is:
D. [tex]\((3, 5)\)[/tex]
