To determine the axis of symmetry for the quadratic function [tex]\( h(x) = 6x^2 - 60x + 147 \)[/tex], we can use the formula for the axis of symmetry for a quadratic equation of the form [tex]\( ax^2 + bx + c \)[/tex]. The formula is:
[tex]\[ x = -\frac{b}{2a} \][/tex]
Here, [tex]\(a = 6\)[/tex] and [tex]\(b = -60\)[/tex]. Plugging these values into the formula, we get:
[tex]\[ x = -\frac{-60}{2 \cdot 6} \][/tex]
Simplify the expression inside the fraction:
[tex]\[ x = \frac{60}{12} \][/tex]
Now, divide 60 by 12:
[tex]\[ x = 5 \][/tex]
So, the axis of symmetry for the quadratic function [tex]\( h(x) = 6x^2 - 60x + 147 \)[/tex] is [tex]\( x = 5 \)[/tex].
Among the given choices:
- [tex]\( x = -5 \)[/tex]
- [tex]\( x = -3 \)[/tex]
- [tex]\( x = 3 \)[/tex]
- [tex]\( x = 5 \)[/tex]
The correct answer is [tex]\( x = 5 \)[/tex].
