Question

What are the vertex, axis of symmetry, maximum or
minimum value, and range of y=-5(x+2)^2-8?

please explain to me how you would solve this..I don't really understand.

The answer is given..
The vertex is (-2, -8);
the axis of symmetry is
x= -2; k= -8 is the
maximum value; the domain
is all real numbers; the range
is all real numbers less than or equal to -8.

Answer 1

y = a(x-h)^2 +k

y = -5(x+2)^2 - 8

Since a is negative, we know that the parabola will face down, so we will have a maximum and not a minimum

The vertex is given as (-h,k)
You have a -2 because it has to be the opposite of 2 and -8 for k because it is supposed to be the same sign. (-2,-8)

axis of symmetry is always = to -h which is the x-value. If you folded the parabola along that line, it would match showing its symmetry.

Since we determined earlier that the parabola is facing down, we have a maximum which is the y value of -8.

For a parabola the domain is always all real numbers. This is true because there is no possible number that will make the result undefined.

Since -8 is the greatest value for y then the range is all real numbers less than or equal to -8

You can also look at the parabola in ax^2+bx + c form. You would do that by squaring x+2 and multiplying by -5