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 [tex]x = \frac{-b}{2a}[/tex]
Given the quadratic equation:
[tex]h(x) = -2x^2+12x-3[/tex]
Compare above equation with general quadratic equation [tex]ax^2+bx+c[/tex] 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: [tex]x =-\frac{b}{2a}[/tex] ......[1]
Substitute the value of a and b in [1],
[tex]x = \frac{-12}{2 \cdot -2} = \frac{12}{4} = 3[/tex]
therefore, the axis of symmetry of [tex]h(x) = 2x^2+12x-3[/tex] is, x = 3
