Answer:
Characteristic of the axis of symmetry:
It is the line of symmetry of a parabola that divides a parabola into two equal halves that are reflections of each other about the line of symmetry.
It intersects a parabola at its vertex.
* It is a vertical line with the equation of \(x = \frac{-b}{2a}\)
Given the quadratic equation:
\(h(x) = -2x^2+12x-3\)
Compare above equation with general quadratic equation \(ax^2+bx+c\) to find the values of a and b;
then the value of a= -2 and b = 12
Then, the axis of symmetry is given by: \(x =-\frac{b}{2a}\) ......[1]
Substitute the value of a and b in [1],
\(x = \frac{-12}{2 \cdot -2} = \frac{12}{4} = 3\)
therefore, the axis of symmetry of \(h(x) = 2x^2+12x-3\) is, x = 3
