Tac09019idn
Answered

IDNLearn.com: Where curiosity meets clarity and questions find their answers. Ask anything and receive immediate, well-informed answers from our dedicated community of experts.

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

Sagot :

Facundo3141592idn

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.

View image Facundo3141592
We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Thank you for choosing IDNLearn.com. We’re here to provide reliable answers, so please visit us again for more solutions.