Question
Write the equation of the quadratic function in the graph in standard form.
(-2, 5)
(2 points)
The standard form of the quadratic is y=
𝑦
=
x2+
𝑥
2
+
x+
𝑥
+
.
(-2, 5)
(2 points)
The standard form of the quadratic is y=
𝑦
=
x2+
𝑥
2
+
x+
𝑥
+
.
Answers
GPT-4o mini
To convert a quadratic function into standard form, we generally represent it as:
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola.
Given that you provided a point \((-2, 5)\), we can assume this is the vertex of the quadratic function. Thus, we will substitute \(h = -2\) and \(k = 5\):
From the vertex form, we can write:
\[
y = a(x + 2)^2 + 5
\]
To find the value of \(a\), we need another point on the graph, but that point hasn't been provided. Let's assume you have a specific point or conditions that can help determine \(a\).
For now, if we just wanted the general form, we can expand the vertex form:
1. Start with:
\[
y = a(x + 2)^2 + 5
\]
2. Expand \((x + 2)^2\):
\[
y = a(x^2 + 4x + 4) + 5
\]
3. Distribute \(a\):
\[
y = ax^2 + 4ax + 4a + 5
\]
So in standard form \(y = ax^2 + bx + c\), we get:
\[
y = ax^2 + 4ax + (4a + 5)
\]
Now if you provide another point on the curve or additional conditions, we can find the specific value of \(a\) and complete the equation. Alternatively, if you want to specify just \(a\) as 1 or another value, we can easily substitute it in.
\[
y = a(x - h)^2 + k
\]
where \((h, k)\) is the vertex of the parabola.
Given that you provided a point \((-2, 5)\), we can assume this is the vertex of the quadratic function. Thus, we will substitute \(h = -2\) and \(k = 5\):
From the vertex form, we can write:
\[
y = a(x + 2)^2 + 5
\]
To find the value of \(a\), we need another point on the graph, but that point hasn't been provided. Let's assume you have a specific point or conditions that can help determine \(a\).
For now, if we just wanted the general form, we can expand the vertex form:
1. Start with:
\[
y = a(x + 2)^2 + 5
\]
2. Expand \((x + 2)^2\):
\[
y = a(x^2 + 4x + 4) + 5
\]
3. Distribute \(a\):
\[
y = ax^2 + 4ax + 4a + 5
\]
So in standard form \(y = ax^2 + bx + c\), we get:
\[
y = ax^2 + 4ax + (4a + 5)
\]
Now if you provide another point on the curve or additional conditions, we can find the specific value of \(a\) and complete the equation. Alternatively, if you want to specify just \(a\) as 1 or another value, we can easily substitute it in.