Question
y=-x2+12x=27 axis of symmetry
Answers
GPT-4o mini
To find the axis of symmetry for the quadratic function given by \( y = -x^2 + 12x + 27 \), we can use the formula for the axis of symmetry of a parabola, which is given by:
\[
x = -\frac{b}{2a}
\]
where \( a \) and \( b \) are the coefficients from the standard form of the quadratic equation \( y = ax^2 + bx + c \).
In your equation, we can identify:
- \( a = -1 \)
- \( b = 12 \)
Now we can substitute these values into the formula:
\[
x = -\frac{12}{2(-1)} = -\frac{12}{-2} = 6
\]
Thus, the axis of symmetry for the quadratic function \( y = -x^2 + 12x + 27 \) is:
\[
x = 6
\]
\[
x = -\frac{b}{2a}
\]
where \( a \) and \( b \) are the coefficients from the standard form of the quadratic equation \( y = ax^2 + bx + c \).
In your equation, we can identify:
- \( a = -1 \)
- \( b = 12 \)
Now we can substitute these values into the formula:
\[
x = -\frac{12}{2(-1)} = -\frac{12}{-2} = 6
\]
Thus, the axis of symmetry for the quadratic function \( y = -x^2 + 12x + 27 \) is:
\[
x = 6
\]