Question
What is the vertex for of the graph equation?
The axis of symmetry is at 2, -14. y =(x-_)^2+_
The axis of symmetry is at 2, -14. y =(x-_)^2+_
Answers
GPT-4o mini
The vertex form of a quadratic equation is given by the equation:
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the quadratic function.
Given that the axis of symmetry is at (2, -14), this suggests that the vertex of the parabola is at the point \((h, k) = (2, -14)\).
Thus, we can substitute \(h\) and \(k\) into the vertex form equation:
\[
y = a(x - 2)^2 - 14
\]
The value of \(a\) determines the width and direction of the parabola. If you have additional information about the parabola, such as a specific point it passes through, you can determine the value of \(a\).
In summary, the vertex form of the equation is:
\[
y = a(x - 2)^2 - 14
\]
For the blanks in your question \(y = (x - _)^2 + _\), it would be:
\((x - 2)\) and \(-14\).
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the quadratic function.
Given that the axis of symmetry is at (2, -14), this suggests that the vertex of the parabola is at the point \((h, k) = (2, -14)\).
Thus, we can substitute \(h\) and \(k\) into the vertex form equation:
\[
y = a(x - 2)^2 - 14
\]
The value of \(a\) determines the width and direction of the parabola. If you have additional information about the parabola, such as a specific point it passes through, you can determine the value of \(a\).
In summary, the vertex form of the equation is:
\[
y = a(x - 2)^2 - 14
\]
For the blanks in your question \(y = (x - _)^2 + _\), it would be:
\((x - 2)\) and \(-14\).