To find the line of symmetry for the quadratic equation [tex]\( y = -16x^2 + 64x + 80 \)[/tex], we follow specific steps:
### Step-by-Step Solution:
1. Identify the Coefficients:
The given quadratic equation is in the standard form [tex]\( y = ax^2 + bx + c \)[/tex].
- Coefficient [tex]\( a \)[/tex] is the coefficient of [tex]\( x^2 \)[/tex], which is [tex]\( a = -16 \)[/tex].
- Coefficient [tex]\( b \)[/tex] is the coefficient of [tex]\( x \)[/tex], which is [tex]\( b = 64 \)[/tex].
- Coefficient [tex]\( c \)[/tex] is the constant term, which is [tex]\( c = 80 \)[/tex].
2. Formula for the Line of Symmetry:
The line of symmetry (also known as the axis of symmetry) for a quadratic equation [tex]\( y = ax^2 + bx + c \)[/tex] occurs at [tex]\( x = -\frac{b}{2a} \)[/tex].
3. Substitute the Values:
Here, we substitute [tex]\( a = -16 \)[/tex] and [tex]\( b = 64 \)[/tex] into the formula [tex]\( x = -\frac{b}{2a} \)[/tex].
[tex]\[
x = -\frac{64}{2 \cdot (-16)}
\][/tex]
4. Simplify the Equation:
Simplify the expression inside the fraction:
[tex]\[
x = -\frac{64}{-32}
\][/tex]
[tex]\[
x = 2
\][/tex]
### Conclusion:
The line of symmetry for the quadratic equation [tex]\( y = -16x^2 + 64x + 80 \)[/tex] is [tex]\( x = 2 \)[/tex].
So, the line of symmetry is [tex]\( x = 2 \)[/tex].
