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]
