Question

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

Answer 1

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

Answer 2

what equation?

Answer 3

what class is this for?

Answer 4

college algebra

Answer 5

can you expand the right hand side?

Answer 6

yes

Answer 7

up

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

My bad, the leading coefficient.

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

Yeah, the graph someone attached helped. Thanks everyone

Answer 17

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

Answer 18

Cyter that is calculus. She is in college algebra.

Answer 19

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

Answer 20

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.

Answer 21

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

Answer 22

i think it's narrower

Answer 23

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