$$ 3: 24 $$ 824 Done © deltamath.com Assignment Overview 1 $$ \therefore $$ DeltaMath Score: 7/12 Penalty: none Axis of Symmetry and Vertex (with Formula) Question () Video Examples Find the equation of the axis of symmetry of the following parabola algebraically. $$ y=2 x^{2}-20 x+66 $$ Answer Attempt 2 out of 3 $$ \square $$ Submit Answer Still Stuck? Copyright ©2025 DeltaMath.com All Rights Reserved. Terms \& Policies

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UpStudy AI · Accepted Answer

To find the **axis of symmetry** of the parabola defined by the quadratic equation:

$$
y = 2x^{2} - 20x + 66
$$

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** $$ a $$ and $$ b $$ in the quadratic equation:
   
   $$
   a = 2 \quad \text{and} \quad b = -20
   $$

2. **Plug the values of $$ a $$ and $$ b $$ into the formula**:

$$
   x = -\frac{-20}{2 \times 2}
   $$

3. **Simplify the equation**:

$$
   x = \frac{20}{4} = 5
   $$

**Conclusion:**

The equation of the **axis of symmetry** for the given parabola is:

$$
\boxed{x=5}
$$

This means the parabola is symmetric about the vertical line $$ x = 5 $$.
The axis of symmetry is $$ x = 5 $$.

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