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 + _. Refrain from putting letters in the empty slots
y = _x^2 + _x + _. Refrain from putting letters in the empty slots
Answers
GPT-4o mini
To write the equation of a quadratic function in standard form \( y = ax^2 + bx + c \), we also need the vertex form which is given by:
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola. The axis of symmetry is given as \(x = 3\), which means \(h = 3\).
To complete the equation, we need the value of \(a\) and \(k\). If you have additional information such as the vertex or another point through which the parabola passes, please provide that so we can find the specific values for \(a\) and \(k\).
In the absence of \(k\) (the y-coordinate of the vertex) and \(a\), we would just leave those values as placeholders. The general structure you could follow would be:
\[ y = a(x - 3)^2 + k \]
Expanding this, we get:
\[ y = a(x^2 - 6x + 9) + k \]
Thus:
\[ y = ax^2 - 6ax + (9a + k) \]
From this, we can see:
- The coefficient of \(x^2\) is \(a\),
- The coefficient of \(x\) is \(-6a\),
- The constant term is \(9a + k\).
If you provide \(a\) and \(k\), we can fill in the exact values. In this case, please let me know if you have more information or if you want a specific example!
\[ y = a(x - h)^2 + k \]
where \((h, k)\) is the vertex of the parabola. The axis of symmetry is given as \(x = 3\), which means \(h = 3\).
To complete the equation, we need the value of \(a\) and \(k\). If you have additional information such as the vertex or another point through which the parabola passes, please provide that so we can find the specific values for \(a\) and \(k\).
In the absence of \(k\) (the y-coordinate of the vertex) and \(a\), we would just leave those values as placeholders. The general structure you could follow would be:
\[ y = a(x - 3)^2 + k \]
Expanding this, we get:
\[ y = a(x^2 - 6x + 9) + k \]
Thus:
\[ y = ax^2 - 6ax + (9a + k) \]
From this, we can see:
- The coefficient of \(x^2\) is \(a\),
- The coefficient of \(x\) is \(-6a\),
- The constant term is \(9a + k\).
If you provide \(a\) and \(k\), we can fill in the exact values. In this case, please let me know if you have more information or if you want a specific example!