Can anyone help me with finding the domain and range for this quadratic equation y = –x^2 – 14x – 52?

Question

anonymous · Answer

$$b^2 -4ac \geq 0$$

anonymous · Answer

What..?

anonymous · Answer

Take it to the completed square form

anonymous · Answer

How?

anonymous · Answer

Factorize it

anonymous · Answer

y = –x^2 – 14x – 52
   = -(x^2+14x)-52
    =-(x^2+2*x*7+7^2-7^2)-52
    = -{(x+7)^2-49}-52
     =-(x+7)^2-3

anonymous · Answer

thats the completed square form

anonymous · Answer

Now, domain is x E R.......

anonymous · Answer

For range, (x+7)^2>=0
                 -(x+7)^2<=0
                 -(x+7)^2-3<=-3
                   y<=-3

anonymous · Answer

got it?

precal · Answer

I always look at the graphs when determining the domain and range

precal · Answer

precal · Answer

domain is all real numbers
range is all numbers less than and equal to -3 
just like sauravshakya stated

precal · Answer

use the above link if you do not own a graphing calculator

anonymous · Answer

Domain is R becoz...there is no...Restrictions...)) in the given equation

precal · Answer

yes and domain is all real numbers because all of the x's are being used on the number line to plot the function