Question

Describe the graph of the function f(x) = x3 − 15x2 + 68x − 96. Include the y-intercept, x-intercepts, and the shape of the graph.

Answer 1

Do you guys understand it what to do?

Answer 2

these can be tricky
Its easy to find the y-intercept by plugging x = 0 and working the function out.

Answer 3

is it like finding the zeros of the function?

Answer 4

I don't know if it is then I can solve this

Answer 5

what are you learning in your class lessons?

Answer 6

to find the zeros ( the x -intercepts) we can use trial and error . retricethe last number is -96 you might try x = 3 or 4 to start with

Answer 7

f(3) = 3^3 - 15(3)^2 + 68*3 - 96
= 27 - 135 + 204 - 96 = 0

thats a bit of luck
one of the zeros is 3

Answer 8

that means one of the factors of the function is x - 3
so we can divide x - 3 into the function using synthetic or long division

Answer 9

I am sorry I was away from my computer for a bit, let me see what you said.

Answer 10

Thanks! That really helped!

Answer 11

yw

Answer 12

this will have up to 3 real roots
If you know calculs you can also find the turning points on the graph
Have you learnt any calculus?

Answer 13

I have done the long division and I can tell you there are 2 more real roots and they are both whole numbers.

Answer 14

gotta go