Question
Can you find the equation of a parabola that is vertically stretched by 2, sitting with its vertex on the x-axis at x = -3
Answers
Answered by
GPT-4o mini
To find the equation of a vertically stretched parabola with its vertex on the x-axis at \( x = -3 \), we can start with the standard form of a parabola's equation that opens upwards, which is:
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola.
1. Since the vertex is on the x-axis at \( x = -3 \), we have \( h = -3 \).
2. Additionally, since the vertex is on the x-axis, \( k = 0 \).
3. The equation becomes:
\[
y = a(x + 3)^2
\]
4. The problem states that the parabola is vertically stretched by 2. This means that the value of \( a \) should be adjusted to indicate that stretching. If the standard form is stretched vertically by a factor of 2, \( a \) should be 2. So we have:
\[
a = 2
\]
5. Substituting \( a \) into the equation gives us:
\[
y = 2(x + 3)^2
\]
Therefore, the equation of the parabola is:
\[
y = 2(x + 3)^2
\]
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola.
1. Since the vertex is on the x-axis at \( x = -3 \), we have \( h = -3 \).
2. Additionally, since the vertex is on the x-axis, \( k = 0 \).
3. The equation becomes:
\[
y = a(x + 3)^2
\]
4. The problem states that the parabola is vertically stretched by 2. This means that the value of \( a \) should be adjusted to indicate that stretching. If the standard form is stretched vertically by a factor of 2, \( a \) should be 2. So we have:
\[
a = 2
\]
5. Substituting \( a \) into the equation gives us:
\[
y = 2(x + 3)^2
\]
Therefore, the equation of the parabola is:
\[
y = 2(x + 3)^2
\]
There are no human answers yet. A form for humans to post answers is coming very soon!