Question

FAN AND MEDAL
2.Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14

Answer 1

@Dangazzm @DullJackel09 @Daniee_Bruhh

Answer 2

I have no idea how to do this one love! But I wish you the best of luck :) <3

Answer 3

thank you for trying

Answer 4

@Astrophysics @AloneS @Abmon98 @Atsie @ShadowLegendX

Answer 5

Ok so I picked the top equation g(x) = x3 − x2 − 4x + 4 I like to use https://www.desmos.com/calculator to visualize my graphs and check my answers!

So g(x) is just like saying y, or at least that's how I think of it and I think that's best to explain it.

SO first thing I'll explain with this is when does it cross the Y axis? Well it's when X=0 right? Because the Y axis is right there at X=0. So we plug in 0 for x

\[y = 0^3-0^2-4(0) + 4\]
Anything times 0 is 0 so... y = 4! Cool! We look at our graph we did on Desmos and see, yep right there (0,4)

Next up we will find the X intercepts by setting Y = 0

\[0 = X^3 - X^2 -4x+4\]
Hmm let's try factoring this out...
So first we group our terms.
\[0 = (x^3-x^2) + (-4x + 4)\]
Notice how I kept the negative on that -4x.
\[0 = x^2(x-1) - 4(x-1)\]

There we got a (x-1) in common so that's a factor!

\[0 = (x^2-4)(x-1)\]
Let's finish up factoring the X^2-4 since this is a difference of 2 squares it's easy enough.
\[0 = (x+2)(x-2)(x-1)\]

Now we set each of these factors to 0 to find out when it crosses the x axis so for example

0 = (x+2)
0 = x-2
0 = x-1

We see these three point on the graph too! So we know we did good!


Sorry it took so long to type but hopefully you get it after this. Any questions please ask!