Question
Find the equation of the axis of symmetry of the following parabola using graphing technology.
and = x^2 + 2+ 8x + 11
and = x^2 + 2+ 8x + 11
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GPT-4o mini
To find the equation of the axis of symmetry for the given quadratic function \( y = x^2 + 2 + 8x + 11 \), we first rewrite the equation in a standard form.
Combining like terms:
\[
y = x^2 + 8x + 13
\]
For a quadratic equation in the standard form \( y = ax^2 + bx + c \), the formula for the axis of symmetry is given by:
\[
x = -\frac{b}{2a}
\]
In this equation:
- \( a = 1 \)
- \( b = 8 \)
Now substituting these values into the formula:
\[
x = -\frac{8}{2 \times 1} = -\frac{8}{2} = -4
\]
Thus, the equation of the axis of symmetry is:
\[
x = -4
\]
You can verify this by using graphing technology to visualize the parabola. The axis of symmetry will be a vertical line at \( x = -4 \).
Combining like terms:
\[
y = x^2 + 8x + 13
\]
For a quadratic equation in the standard form \( y = ax^2 + bx + c \), the formula for the axis of symmetry is given by:
\[
x = -\frac{b}{2a}
\]
In this equation:
- \( a = 1 \)
- \( b = 8 \)
Now substituting these values into the formula:
\[
x = -\frac{8}{2 \times 1} = -\frac{8}{2} = -4
\]
Thus, the equation of the axis of symmetry is:
\[
x = -4
\]
You can verify this by using graphing technology to visualize the parabola. The axis of symmetry will be a vertical line at \( x = -4 \).
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