Question
Write the equation of the quadratic function in the graph in standard form. The axis of symmetry is at 3. -1.
y = _x^2 + _x + _
y = _x^2 + _x + _
Answers
GPT-4o mini
To write the equation of a quadratic function in standard form \( y = ax^2 + bx + c \), we can use the information provided: the axis of symmetry is at \( x = 3 \).
The axis of symmetry for a quadratic function in the standard form can be calculated using the formula:
\[
x = -\frac{b}{2a}
\]
Given that the axis of symmetry is at \( x = 3 \), this means:
\[
3 = -\frac{b}{2a}
\]
From this, we can rearrange to find \( b \) in terms of \( a \):
\[
b = -6a
\]
To find the complete equation, we also need to know another point on the graph or the value of the vertex or some specific characteristics of the function. However, without additional information, we can only represent the quadratic in terms of \( a \).
Thus, the equation can be expressed as:
\[
y = ax^2 - 6ax + c
\]
where \( a \) and \( c \) are constants that need further information to be determined.
If you have further details (like the vertex or another point on the graph), please provide them.
The axis of symmetry for a quadratic function in the standard form can be calculated using the formula:
\[
x = -\frac{b}{2a}
\]
Given that the axis of symmetry is at \( x = 3 \), this means:
\[
3 = -\frac{b}{2a}
\]
From this, we can rearrange to find \( b \) in terms of \( a \):
\[
b = -6a
\]
To find the complete equation, we also need to know another point on the graph or the value of the vertex or some specific characteristics of the function. However, without additional information, we can only represent the quadratic in terms of \( a \).
Thus, the equation can be expressed as:
\[
y = ax^2 - 6ax + c
\]
where \( a \) and \( c \) are constants that need further information to be determined.
If you have further details (like the vertex or another point on the graph), please provide them.