From the equation, find the axis of symmetry of the parabola.

[tex]\[ y = -4x^2 + 24x - 35 \][/tex]

A. [tex]\( x = 1 \)[/tex]
B. [tex]\( x = -1 \)[/tex]
C. [tex]\( x = 3 \)[/tex]
D. [tex]\( x = -3 \)[/tex]



Answer :

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]