Question

What is the domain and range of the quadratic equation y = –x^2 – 14x – 52?

Answer 1

domain is all real numbers (as for any poly function)

Answer 2

Putting it into vertex form
-(x^2+14x) - 52
-(x^2 + 14x + 49) - 52 + 49
-(x+7)^2 - 3
So y ≤ -3

Answer 3

The range is in in\[(-\infty,-3]\]terval notation

Answer 4

this has a maxm value at vertex - the graph is open downwards

vertex is at (-7,-3)
domain is all real numbers
range is f(x) < = -3

Answer 5

Vertex has coordinates x--b/2a \[x=-14/2(-1)=-7\]Vertex has y-coordinate y=f(-b/2a) \[y=-(-7)^2-14(-7)-52=-3\] Since th parabola opens downward, the vertex is max