Poopeyidn
Answered

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When the function is given in vertex form [tex][tex]$y=a(x-h)^2+k$[/tex][/tex], how is the vertex found?

A. (k, h)
B. (h, k)
C. (x, y)
D. (y, x)

Please select the best answer from the choices provided:
A, B, C, or D.

Sagot :

GinnyAnsweridn
To find the vertex of a quadratic function given in vertex form, we must understand what each parameter in the vertex form equation represents. The vertex form of a quadratic function is written as:

[tex]\[ y = a(x - h)^2 + k \][/tex]

Here:
- [tex]\(a\)[/tex] is a coefficient that affects the width and direction of the parabola (whether it opens upwards or downwards).
- [tex]\(h\)[/tex] represents the x-coordinate of the vertex.
- [tex]\(k\)[/tex] represents the y-coordinate of the vertex.

The vertex form explicitly highlights the vertex of the parabola. The vertex [tex]\((h, k)\)[/tex] is a crucial point because it is either the highest or lowest point on the graph of the quadratic function, depending on the sign of [tex]\(a\)[/tex].

To find the vertex from the equation:

1. Identify the values of [tex]\(h\)[/tex] and [tex]\(k\)[/tex] directly from the equation.
2. The vertex [tex]\((h, k)\)[/tex] is constructed from these values.

Hence, the vertex of the quadratic function in this form is given by the coordinates [tex]\((h, k)\)[/tex].

Therefore, the correct answer is:

C. [tex]\((h, k)\)[/tex]
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