1. Graph the function. Then identify the domain and range of the function.
y= -1/2x^2

2. A person walking across a bridge accidentally drops an orange into the river below from a height of 40 ft. The function h= -16t^2+40 give the orange's approximate height h above the water, in feet, after t seconds. Graph the function. In how many seconds will the orange hit the water?

Ps. Explain both answers

Question

1. Graph the function. Then identify the domain and range of the function.
y= -1/2x^2

2. A person walking across a bridge accidentally drops an orange into the river below from a height of 40 ft. The function h= -16t^2+40 give the orange's approximate height h above the water, in feet, after t seconds. Graph the function. In how many seconds will the orange hit the water?

Ps. Explain both answers

johnweldon1993 · Answer

|dw:1395932281237:dw|
That is the graph...it is slightly "fatter" than just -x^2

Domain....what numbers on the 'x' axis will this reach? (ps..the graph doesn't stop there...those go on forever)

krazzikitten69 · Answer

I don't know:|

johnweldon1993 · Answer

That's alright :)

Alright so...it will reach ALL of the numbers on the x-axis....why? well because like I said that parabola will go on forever...always going always going...of course going DOWN...but still...so it will reach every number on that x-axis eventually..

so the domain is (-infinity , infinity)

johnweldon1993 · Answer

Also you can think about it like this.....is there any number you can plug into -1/2x^2 that will make it Undefined? that will make it not a real number? no...so the domain would be any number (-infinity , infinity)

johnweldon1993 · Answer

Now...RANGE...

Range is the y-axis....

See how the graph starts from the origin (0,0) and just goes down? Well (sadly) it never touches any of the positive y-axis...it starts at 0...and goes down to -infinity...

So the range...is (0 , -infinity)

johnweldon1993 · Answer

Another way to think about THAT one...is ANY number you plug into that equation -1/2x^2

lets do 10

-1/2(10)^2 = -1/2(100) = -50

What happened there? it became a negative number...

even if we plug in -10

-1/2(-10)^2 =   -1/2(100) = -50

Again -50...why? because when you square a negative number...it becomes positive...but we still had to deal with that -1/2 part in front...

So see...this equation will never be a POSITIVE number...so its range again is (0 , -infinity)

johnweldon1993 · Answer

Let me know if that makes sense @krazzikitten69  :)

krazzikitten69 · Answer

Kind of.. so what would I say my answer would be for a quick explanation

johnweldon1993 · Answer

You would say Domain = (-infinity , infinity) 
And Range = (0 , -infinity)

krazzikitten69 · Answer

ohh okay its making sense now:) Can you help me with the other?

johnweldon1993 · Answer

Sure :)

so the graph would look something like

|dw:1395933134046:dw|