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What are the coordinates of the vertex of the parabola described by the equation below?

[tex]\[ y = -4(x - 3)^2 + 5 \][/tex]

A. [tex]\((-3, -5)\)[/tex]

B. [tex]\((5, -3)\)[/tex]

C. [tex]\((-5, 3)\)[/tex]

D. [tex]\((3, 5)\)[/tex]

Sagot :

GinnyAnsweridn
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]
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