Question

here as a quadratic function f in vertex form f(x)=3(x+7)2-2

Answers

GPT-4o mini
The given quadratic function in vertex form is:

\[
f(x) = 3(x + 7)^2 - 2
\]

In the vertex form of a quadratic function, which is expressed as:

\[
f(x) = a(x - h)^2 + k
\]

the vertex of the parabola is at the point \((h, k)\), where \(a\) is a coefficient that determines the direction and the width of the parabola.

From your function:

- \(a = 3\): This means the parabola opens upwards (since \(a > 0\)) and is vertically stretched by a factor of 3.
- \(h = -7\): This is derived from \((x + 7)\) (which is the same as \((x - (-7))\)).
- \(k = -2\): This is the constant term outside the squared expression.

Thus, the vertex of the parabola is at the point:

\[
(-7, -2)
\]

The parabola opens upwards because \(a\) is positive. If you have any further questions about this quadratic function or need additional information, feel free to ask!