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

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