Verified answer

The axis of symmetry occurs at x = -b/(2a) for a parabola of form y = ax^2 + bx + c.

x = -b/(2a) is also the x-value at the vertex

Simply substitute this value into the function to determine the y-value.

for y=-2x^2-8x-5, x = -b/(2a) is x=8/(-4) = -2, and at x=-2, y=3

Hence, axis of symmetry is x = -2 and vertex is (x,y) = (-2,3).

First note that the equation represents a parabola. If you want to see why this is so, do a search for "general equation parabola". Now the equation for the parabola is in the form:

y = ax^2 + bx + c, a,b,c constants

The equation for the axis of symmetry is x = -b/(2a). I would like to explain to you why this is so, but unfortunately the explanation involves some basic calculus which is probably a little advanced for you at the moment. Which sucks because this is a formula that you really won't need to remember in the future but you have to for the moment :(

So for the first equation we have a=-2, b=-8, c=-5 (we don't care about c though). Therefore the axis of symmetry is:

x = -(-8) / (2*(-2)) = 8 / (-4) = -2, the vertical line x = -2

To find the coordinates of the vertex, plug in x = -2 into the equation and solve for y:

y = -2(-2)^2 - 8(-2) - 5 = -2(4) + 16 - 5 = -8 + 16 - 5 = 3

So the coordinates of the vertex are x=-2, y=3 also written as (-2, 3)

The second problem is similar, except that you must also determine whether the vertex is a maximum or minimum (the axis of symmetry passes through the vertex). The easiest way to tell whether the vertex is a maximum or minimum is to simply choose a value for x different than the vertex's. If the resulting y value is greater than the vertex the vertex is a minimum, otherwise it is a maximum.

Axis of symmetry: x=-2

Coordinates of vertex: (-2,3)

Axis of symmetry: x = 3/2

It contains a maximum because the parabola opens up.