Question

What is the axis of symmetry of h(x) = –2x2 + 12x – 3?

Answer 1

the axis of symmetry is the x value of the vertex
we have a handy-dandy way of finding that from standard form, ax^2+bx+c=y

for
ax^2+bx+c=y
the x value of the vertex is -b/2a

y=-2x^2+12x-3
-b/2a=-12/(2*-2)=-12/-4=3

x=3 is the axis of symmetry

Answer 2

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 = (-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 =-(b)/(2a)` ......[1]

Substitute the value of a and b in [1],

`x =  (-12)/(2 \cdot -2) = (12)/(4) = 3`

therefore, the axis of symmetry of
`h(x) = 2x^2+12x-3` is, x = 3