need to determine whether the graph of this equation opens upward or downward

- anonymous

need to determine whether the graph of this equation opens upward or downward

- jamiebookeater

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- anonymous

\[y=(x-4)^{2}+5\]

- anonymous

what equation?

- anonymous

what class is this for?

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## More answers

- anonymous

college algebra

- anonymous

can you expand the right hand side?

- anonymous

yes

- anonymous

up

- anonymous

For polynomials, the sign of the coefficient determines what way it opens.

- anonymous

http://www.wolframalpha.com/input/?i=(x-4)^2%2B5

- anonymous

you sure she knows which coefficient you are talking about? and is that an answer for college algbra? =/

- anonymous

My bad, the leading coefficient.

- anonymous

The graph is shifted units to the right, 5 units up and vertically stretched by a factor of 2

- anonymous

I don't understand what astyria is asking? but thanks guys. I just wasn't sure if theres an easy way to tell from looking

- anonymous

The graph is shifted 4 units to the right, 5 units up and vertically stretched by a factor of 2

- anonymous

if i were you mary, I would plot some points (that's probably what you guys are learning)...i'm not sure if what cyter says makes sense to you...good luck

- anonymous

Yeah, the graph someone attached helped. Thanks everyone

- anonymous

take the second derivative of y or d²y/dx², if its positive, then the graph is concave up on an arbitrary interval (a,b)

- anonymous

Cyter that is calculus. She is in college algebra.

- anonymous

i now have to determine whither this point is wider or narrower. \[y=(x-4)^{2}+5\]

- anonymous

The utmost easiest way to determine whether a graph of a polynomial opens up or down is to look at the leading coefficient, which is the coefficient in front of the x^2. If that coefficient is positive the graph opens up, if negative it opens down.

- anonymous

oh ok. oops i typed the same problem. this is the equation I need to figure out if it is wider or narrower than the previous one..\[y=2(x-4)^{2}\]

- anonymous

i think it's narrower

- anonymous

The higher the magnitude of the coefficient, the narrower the graph is. You are correct.

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