Question
On a graph has point(-4,-2). It is downward
y=-(x- ___)^2+. ____
y=-(x- ___)^2+. ____
Answers
Answer
Sorry the vertex is (-4,-2)
Answered by
GPT-4o mini
To put the equation of the parabola in vertex form, we start with the general form:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
Given the point \((-4, -2)\), we can identify the vertex of the parabola:
\[
h = -4 \quad \text{and} \quad k = -2
\]
This allows us to substitute \(h\) and \(k\) into the equation:
\[
y = a(x - (-4))^2 - 2
\]
This simplifies to:
\[
y = a(x + 4)^2 - 2
\]
Next, to find the value of \(a\), we note that since the parabola opens downward, \(a\) must be negative. The exact value of \(a\) will depend on another point that lies on the parabola.
For example, if you assume that the parabola passes through another point, you can substitute that point into the equation to solve for \(a\). However, if you don’t have another point, we cannot determine the exact value of \(a\).
As a response to your placeholders, we can fill them in as follows:
So, the completed equation in terms of the given point is:
\[ y = a(x + 4)^2 - 2 \]
Where:
- The blank for \(h\) is \(-4\).
- The blank for \(k\) is \(-2\).
- \(a\) is the coefficient that needs to be determined based on another point.
Please provide another point if you have one to find the value of \(a\).
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola.
Given the point \((-4, -2)\), we can identify the vertex of the parabola:
\[
h = -4 \quad \text{and} \quad k = -2
\]
This allows us to substitute \(h\) and \(k\) into the equation:
\[
y = a(x - (-4))^2 - 2
\]
This simplifies to:
\[
y = a(x + 4)^2 - 2
\]
Next, to find the value of \(a\), we note that since the parabola opens downward, \(a\) must be negative. The exact value of \(a\) will depend on another point that lies on the parabola.
For example, if you assume that the parabola passes through another point, you can substitute that point into the equation to solve for \(a\). However, if you don’t have another point, we cannot determine the exact value of \(a\).
As a response to your placeholders, we can fill them in as follows:
So, the completed equation in terms of the given point is:
\[ y = a(x + 4)^2 - 2 \]
Where:
- The blank for \(h\) is \(-4\).
- The blank for \(k\) is \(-2\).
- \(a\) is the coefficient that needs to be determined based on another point.
Please provide another point if you have one to find the value of \(a\).
Answered by
GPT-4o mini
No problem! If the vertex is indeed \((-4, -2)\) and the parabola opens downward, we can write the equation in vertex form:
\[
y = a(x - h)^2 + k
\]
Substituting the values of the vertex into the equation:
- \(h = -4\)
- \(k = -2\)
This gives us:
\[
y = a(x + 4)^2 - 2
\]
In this equation, \(a\) must be negative since the parabola opens downwards.
To summarize:
1. The equation structure is \(y = a(x + 4)^2 - 2\).
2. The blank for \(h\) is \(-4\).
3. The blank for \(k\) is \(-2\).
4. The final equation looks like:
\[
y = a(x + 4)^2 - 2
\]
If you have a specific point through which the parabola passes, we can further determine the exact value of \(a\). Otherwise, \(a\) remains unspecified but is negative based on the direction of the parabola.
\[
y = a(x - h)^2 + k
\]
Substituting the values of the vertex into the equation:
- \(h = -4\)
- \(k = -2\)
This gives us:
\[
y = a(x + 4)^2 - 2
\]
In this equation, \(a\) must be negative since the parabola opens downwards.
To summarize:
1. The equation structure is \(y = a(x + 4)^2 - 2\).
2. The blank for \(h\) is \(-4\).
3. The blank for \(k\) is \(-2\).
4. The final equation looks like:
\[
y = a(x + 4)^2 - 2
\]
If you have a specific point through which the parabola passes, we can further determine the exact value of \(a\). Otherwise, \(a\) remains unspecified but is negative based on the direction of the parabola.