Question

If a parabola opens downwards and has a maximum, and if it has a vertex of (-2,-3) and a y-intercept of (0,-11), what is the axis of symmetry, and what is the maximum value of the function?

Answer 1

Its maximum value is -3 and its axis of symmetry is x = -2.

Explanation:

We can write it in vertex form:

y = a(x + 2)^2 - 3 where a is a constant.

When x = 0 y = -11 (the y-intercept), so:

-11 = a(0 + 2)^2 - 3

-11 = 4a - 3

4a = -8

a = -2

So the equation of the parabola is

y = -2(x + 3)^2 - 3.

Its maximum value is -3 and its axis of symmetry is x = -2.