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