To find the axis of symmetry for the given parabola described by the equation [tex]\( y = -4x^2 + 24x - 35 \)[/tex], follow these steps:
1. Identify the coefficients:
- The quadratic equation is in the form [tex]\( y = ax^2 + bx + c \)[/tex].
- Here, [tex]\( a = -4 \)[/tex], [tex]\( b = 24 \)[/tex], and [tex]\( c = -35 \)[/tex].
2. Use the formula for the axis of symmetry:
- The axis of symmetry for a parabola given by the equation [tex]\( y = ax^2 + bx + c \)[/tex] can be found using the formula:
[tex]\[
x = \frac{-b}{2a}
\][/tex]
3. Substitute the coefficients into the formula:
- Plug in the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[
x = \frac{-b}{2a} = \frac{-24}{2(-4)}
\][/tex]
4. Simplify the equation:
- Calculate the denominator:
[tex]\[
2(-4) = -8
\][/tex]
- Then divide:
[tex]\[
x = \frac{-24}{-8} = 3
\][/tex]
Therefore, the axis of symmetry is [tex]\( x = 3 \)[/tex].
The correct answer is:
c. [tex]\( x = 3 \)[/tex]
