Graph the functions y = x and y=2square root x on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.
2007-01-20 04:08:43 · 9 answers · asked by Lana G 1 in Science & Mathematics ➔ Mathematics
y = x is simply the line starting at the origin with slope 1.
y = 2 sqr(x) is the graph of sqr(x) stretched vertically by a factor of 2.
There are two points of intersection: (0,0) and (4,2)
(0,0) is trivial, while when x = 4, the first equation gives y = 4, while the second yields y = 2*sqr(4) = 2*2 = 4
2007-01-20 04:15:32 · answer #1 · answered by JasonM 7 · 3⤊ 0⤋
The intersection points are at (0,0) and (4,4) and here's the reasons why:
0=0
0=2√0
0=2(0)
0=0
4=4
4=2√4
4=2(2)
4=4
I did this by pluging in numbers for x and then graphed both equations on graphing paper, and then I checked the answer on the graphing calculator, which proved the answer was correct!
2007-01-20 04:31:58 · answer #2 · answered by Anonymous · 0⤊ 0⤋
I would but I can't put a graph on the computer.
But, I'll tell you how.
ok you probably have a graphing calculator. so go to the top button that says...Y=
and in the slot put X
then go to the next on and put in 2 squared button and X
then push GRAPH
it will put it on there. Then to get the points that you need to graph on your graph paper...push the yellow button 2nd and GRAPH...which is actually table. It will give you several (X,Y) examples to use.
Good luck. And Algebra gets the best of all of us...or the worst.
2007-01-20 04:16:53 · answer #3 · answered by Anonymous · 0⤊ 0⤋
To find out where they intersect you should set them equal to one another.
x = 2sqrtx
x/2 = sqrtx (divide both sides by two)
(x/2)^2 = x (square both sides to get rid of the sqrt)
x^2/4 = x
x^2 = 4x (multiply both sides by four)
x^2 - 4x = 0 (bring the 4x over to make it equal to zero)
x( x-4) = 0 (take out any common factors
x= 0 x= 4
so they intersect at (0,0) and (4,4) . (get this by plugging the x answers back into the orignal formulas).
2007-01-20 04:17:34 · answer #4 · answered by junglegrl44 2 · 0⤊ 0⤋
You need a graph
By calculation>>
y = x
y = sqrt(x)
Substitution
x = sqrt(x)
x - sqrt(x) = 0
sqrt(x) [sqrt(x) - 1] = 0
sqrt(x) = 0 and sqrt(x) - 1 = 0
x = 0, hence y = 0
and
x = 1, hence y = 1
Points of intersection
(0, 0) and (1, 1)
2007-01-20 04:17:17 · answer #5 · answered by Sheen 4 · 0⤊ 0⤋
y = x is a line, it consists of the points (1|1), (2|2), (3|3) etc.
(like this: http://img.sparknotes.com/figures/3/38f8bc3b42ee5deba6aa2de65eeb48dd/y=x.gif)
y = 2 * Sqrt(x) looks similar to this: http://home.att.net/~srschmitt/precalc/precalc-fig10-02.gif
2007-01-20 04:15:28 · answer #6 · answered by eva 3 · 0⤊ 0⤋
Hang in there, you'll get through it.
2007-01-20 04:16:09 · answer #7 · answered by chazzer 5 · 0⤊ 0⤋
Yeah I hate algebra. UGHHHH. I dont get it at all.
2007-01-20 04:13:07 · answer #8 · answered by Its Me!!! 1 · 0⤊ 2⤋
cheat from someone else its easy
2007-01-20 04:32:08 · answer #9 · answered by BENNETH[[98]] 2 · 1⤊ 2⤋