Question

What is the domain and range of the quadratic equation y = -x2 - 14x - 52?

I know the domain is all real numbers, but I'm stumped on how to find the range. Help?

Answer 1

You could graph it.

Answer 2

I can't -- I don't have any tools to graph with. How do I find it without graphing is what I need to know. :[

Answer 3

domain is all real numbers because it is a polynomial

Answer 4

any polynomial has domain all real numbers, you never have to worry

Answer 5

I know the domain is all real numbers :P I just need to know how I can find the range without graphing, haha.

Answer 6

as for the range, this is a parabola that opens down

Answer 7

Find the vertex.

Answer 8

to the range will be from minus infinity to the highest point on the parabola, which is easy to find

Answer 9

Satellite knows what's up.

Answer 10

the polynomial is
\[y = -x2 - 14x - 52\] and to find the highest point, locate the second coordinate of the vertex. use
\[x=-\frac{b}{2a}\]

Answer 11

in this case
\[a=-1,b=-14,-\frac{b}{2a}=-\frac{-14}{-2}=-7\]

Answer 12

that is the first coordinate, you need the second coordinate which you find by replacing x in the expression
\[y = -x^2 - 14x - 52\] by -7

Answer 13

you get
\[y=-49+98-52=-3\]

Answer 14

so the vertex is (-7,-3), the maximum value of the equation is -3 and the range is
\[(-\infty,-3]\]

Answer 15

let me know if steps are clear

Answer 16

they are :D Thanks so much!

Answer 17

yw
don't forget
\[-\frac{b}{2a}\] is the magic formula