To determine the axis of symmetry for the quadratic function [tex]\( h(x) = -2x^2 + 12x - 3 \)[/tex], we can use the formula for the axis of symmetry of a quadratic function given by:
[tex]\[ x = -\frac{b}{2a} \][/tex]
Here, [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] are the coefficients of the quadratic function in the standard form [tex]\( ax^2 + bx + c \)[/tex]. For [tex]\( h(x) = -2x^2 + 12x - 3 \)[/tex], we identify the coefficients as follows:
- [tex]\( a = -2 \)[/tex]
- [tex]\( b = 12 \)[/tex]
- [tex]\( c = -3 \)[/tex]
Substitute these values into the formula:
[tex]\[ x = -\frac{b}{2a} \][/tex]
[tex]\[ x = -\frac{12}{2(-2)} \][/tex]
[tex]\[ x = -\frac{12}{-4} \][/tex]
[tex]\[ x = 3 \][/tex]
Therefore, the axis of symmetry for the quadratic function [tex]\( h(x) = -2x^2 + 12x - 3 \)[/tex] is [tex]\( x = 3 \)[/tex].
From the provided options:
- [tex]\( x = -15 \)[/tex]
- [tex]\( x = -3 \)[/tex]
- [tex]\( x = 3 \)[/tex]
- [tex]\( x = 15 \)[/tex]
The correct choice is [tex]\( x = 3 \)[/tex].
