Question
Write the equation for the graph in vertex form. The axis of symmetry is at -1, -1.
y =_(x - _)^2 +_
y =_(x - _)^2 +_
Answers
Answered by
GPT-4o mini
To express the equation of a parabola in vertex form, we use the formula:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
Given that the axis of symmetry is at \(x = -1\), this indicates that the vertex's x-coordinate \(h\) is -1. You have also provided the vertex as \((-1, -1)\), so \(k\) is -1 as well.
Now we can substitute \(h\) and \(k\) into the vertex form:
\[ y = a(x + 1)^2 - 1 \]
The value of \(a\) depends on whether the parabola opens upwards or downwards and how wide or narrow it is. If you have more information about the parabola (like another point on the graph), you can determine \(a\). Without that information, the equation remains:
\[ y = a(x + 1)^2 - 1 \]
For example, if we assume \(a = 1\) (a common choice for a standard parabola), the vertex form would be:
\[ y = (x + 1)^2 - 1 \]
So, filling in your request with placeholders for \(a\), we have:
\[ y = a(x + 1)^2 - 1 \]
You can now specify the value of \(a\) to complete the equation.
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
Given that the axis of symmetry is at \(x = -1\), this indicates that the vertex's x-coordinate \(h\) is -1. You have also provided the vertex as \((-1, -1)\), so \(k\) is -1 as well.
Now we can substitute \(h\) and \(k\) into the vertex form:
\[ y = a(x + 1)^2 - 1 \]
The value of \(a\) depends on whether the parabola opens upwards or downwards and how wide or narrow it is. If you have more information about the parabola (like another point on the graph), you can determine \(a\). Without that information, the equation remains:
\[ y = a(x + 1)^2 - 1 \]
For example, if we assume \(a = 1\) (a common choice for a standard parabola), the vertex form would be:
\[ y = (x + 1)^2 - 1 \]
So, filling in your request with placeholders for \(a\), we have:
\[ y = a(x + 1)^2 - 1 \]
You can now specify the value of \(a\) to complete the equation.
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