# What is the axis of symmetry and vertex for the graph y=-2x^2+4x-6?

Jun 30, 2016

the axis of symmetry is x=1; the vertex is (1,-4)

#### Explanation:

In the general equation

$y = a {x}^{2} + b x + c$

the axis of symmetry is given by

$x = - \frac{b}{2 a}$

so, in this case, where a=-2 and b=4, it is:

$x = - \frac{4}{-} 4 = 1$

This also is the x-coordinate of the vertex. To obtain the y-coordinate you can substitute the numeric value (x=1) in the given equation, so

$y = - 2 {\left(1\right)}^{2} + 4 \left(1\right) - 6 = - 2 + 4 - 6 = - 4$