# What is the vertex, axis of symmetry, the maximum or minimum value, and the range of parabola #y = –3(x + 8)^2 + 5#?

##### 1 Answer

1)

2)

3) max =

4) R =

#### Explanation:

1) let's traslate:

so the new parabola is

the vertex of this parabola is in

NB: you could have solve this even without the translation, but it would have been just a waste of time and energy :)

2) The axis of symmetry is the vertical lie passing through the vertex, so

3) It is a downward-facing parabola because the directive coefficient of the quadratic polynomial is negative, so the max is in the vertex, i.e. max=5, and the minimum is

4) Because it is a continuous function, it satisfies Darboux property so the range is

NB: If you don't know Darboux property, it is trivial to prove that if