To determine the coordinates of the vertex of the parabola given by the equation:
[tex]\[
y = -4(x-3)^2 + 5
\][/tex]
we need to compare this equation to the standard form of a parabola equation:
[tex]\[
y = a(x-h)^2 + k
\][/tex]
In the standard form, [tex]\((h, k)\)[/tex] represents the vertex of the parabola.
Given the equation [tex]\( y = -4(x-3)^2 + 5 \)[/tex]:
1. Identify the value of [tex]\(h\)[/tex] and [tex]\(k\)[/tex] from the equation. The general form is [tex]\( a(x-h)^2 + k \)[/tex], and we see:
- [tex]\((x - 3)\)[/tex] implies that [tex]\( h = 3 \)[/tex]
- The constant term outside the squared term is [tex]\( +5 \)[/tex], which means [tex]\( k = 5 \)[/tex]
2. Thus, the coordinates of the vertex [tex]\((h, k)\)[/tex] are:
[tex]\[
(h, k) = (3, 5)
\][/tex]
Therefore, the correct coordinates of the vertex are [tex]\((3, 5)\)[/tex].
The correct answer is:
D. [tex]\((3, 5)\)[/tex]
