Question
dhe equation of the axis of symmetry of the following parabola algebraically. \[ y=-3 x^{2}+24 x-66 \] Answer Attempt 1 out of 2
Ask by Greene Newton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The axis of symmetry is \( x = 4 \).
Solution
To find the **axis of symmetry** of the parabola given by the quadratic equation:
\[
y = -3x^{2} + 24x - 66
\]
we can use the formula for the axis of symmetry of a parabola in the form \( y = ax^{2} + bx + c \):
\[
x = -\frac{b}{2a}
\]
**Step-by-Step Solution:**
1. **Identify the coefficients** \( a \), \( b \), and \( c \):
\[
a = -3,\quad b = 24,\quad c = -66
\]
2. **Apply the axis of symmetry formula**:
\[
x = -\frac{b}{2a} = -\frac{24}{2(-3)} = -\frac{24}{-6} = 4
\]
3. **Write the equation of the axis of symmetry**:
\[
\boxed{x = 4}
\]
**Conclusion:**
The axis of symmetry for the given parabola is the vertical line where \( x = 4 \).
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Simplify this solution Bonus Knowledge
To find the axis of symmetry of the parabola given by the equation \( y = -3x^2 + 24x - 66 \), you can use the formula \( x = -\frac{b}{2a} \). Here, \( a = -3 \) and \( b = 24 \). Plugging in these values, we get: \[ x = -\frac{24}{2 \times -3} = -\frac{24}{-6} = 4. \] So, the axis of symmetry is the vertical line \( x = 4 \). To confirm, you can substitute \( x = 4 \) back into the equation to find the corresponding \( y \)-value. That will define the vertex of the parabola, showing that the axis of symmetry bisects it perfectly!
