Help asappppp? i’m having trouble on wat the 1/4 point is

Mathematics

1 answer:

blagie [28]3 years ago

6 0

Answer:

(-14, 5.5)

Step-by-step explanation:

Perhaps the easiest way to find the 1/4 point is to find (x, y), then find the midpoint between that and M.

(x, y) = 2M -(13, 25) = 2(-5, 12) -(13, 25) = (-23, -1)

Then the 1/4 point is ...

((-23, -1) +M)/2 = ((-23, -1) +(-5, 12))/2 = (-28, 11)/2 = (-14, 5.5)

_____

If we call the end points A(x, y) and B(13, 25), then we know ...

M = (A+B)/2

A = 2M -B . . . . we'll need this in a bit

and the 1/4 point Q is such that ...

(Q -A)/(B -A) = 1/4

4Q -4A = B -A . . . . cross multipliy

Q = (B +3A)/4 = (B +3(2M -B))/4 = (6M -2B)/4 . . . . solve for Q

Q = (3M -B)/2 . . . . reduce the fractions

Q = (3(-5, 12) -(13, 25))/2 = (-28, 11)/2 = (-14, 5.5) . . . as above

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Describe the steps you would take to sketch the graph p(x)=2x^(3)+7x^(2)-3x-18

mojhsa [17]

Answer:

When we have a given function, y = f(x), the general way of graphing the function is finding a lot of coordinate pairs (x, f(x)) and graphing them in a coordinate axis, and then connect them.

So here we have:

p(x) = 2x^(3)+7x^(2)-3x-18

Just let's find the value of p(x) for different values of x, and let's do it.

p(0) = 2*0^(3)+7*0^(2)-3*0-18 = -18

Then the point (0, -18) belongs to the graph

p(1) = 2*1^(3)+7*1^(2)-3*1-18 = 2 + 7 - 3 - 18 = -12

then the point (1, - 12) belongs to the graph.

p(-1) = 2*(-1)^(3)+7*(-1)^(2)-3*(-1)-18 = -2 + 7 + 3 - 18 = -10

then the point (-1, -10) belongs to the graph:

p(2) = 2*2^(3)+7*2^(2)-3*2-18 = 16 + 28 - 6 - 18 = 20

Then the point (2, 20) belongs to the graph

p(-2) = 2*(-2)^(3)+7*(-2)^(2)-3*(-2)-18 = -16 + 28 + 6 - 18 = 0

Then the point (-2, 0) belongs to the graph.

p(-3) = 2*(-3)^(3)+7*(-3)^(2)-3*(-3)-18 = -54 + 63 + 9 - 18 = 0

Then the point (-3, 0) belongs to the graph.

Now that we have 6 points we can graph them and try to connect them.

We also know that this is a cubic polynomial, so we can expect that it changes its direction two times (no more than that) then knowing that we can estimate a shape for the graph, and you will obtain something like the graph of the image below, where I just connected the known points.