To determine the axis of symmetry for the quadratic function [tex]\( f(x) = -4x^2 + 24x + 3 \)[/tex], follow these steps:
1. Identify the coefficients from the quadratic equation [tex]\( ax^2 + bx + c \)[/tex]:
[tex]\[
a = -4, \quad b = 24, \quad c = 3
\][/tex]
2. The formula for the axis of symmetry of a quadratic equation is given by:
[tex]\[
x = -\frac{b}{2a}
\][/tex]
3. Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the formula:
[tex]\[
x = -\frac{24}{2 \cdot (-4)}
\][/tex]
4. Simplify the expression inside the fraction:
[tex]\[
x = -\frac{24}{-8}
\][/tex]
5. Simplify the fraction:
[tex]\[
x = 3
\][/tex]
Therefore, the axis of symmetry for the quadratic function [tex]\( f(x) = -4x^2 + 24x + 3 \)[/tex] is:
[tex]\[
x = 3
\][/tex]
