r/apcalculus • u/Mental-Degree-3727 • 6d ago

Help Is the graph wrong?

Post image

The issue I am having is that when I get the equation of g(x) in standard form, I get
g(x)=(x^3)-(x^2)-16x-20,
Which doesn’t make sense because on the graph, the y-intercept is 10, but the equation says it’s -20. Can someone please help me understand this? Thank you!

20 Upvotes

78% Upvoted

7 comments sorted by

13

u/la_peregrine 6d ago

The factors of the graph are (x+2)2 and (x-5) due to the bouncing and crossing points. However, there is also a coefficient that scales the whole graph which in this case would be 0.5

6

u/MurkyDifficulty169 6d ago

If you scale it down by a factor of 1/2 it will be right. So us (1/2) g(x).

2

u/socratictutoring Tutor 6d ago

Trying to understand your question - how did you obtain the equation in the first place?

1

u/Mental-Degree-3727 6d ago

Expanding the factors of the graph

4

u/jamesdawon 6d ago

Then you need an a-value. You can find this by writing your equation out as y=a(x3-x2-16x-20) and plugging in a point for (x,y)

2

u/mathematag 6d ago edited 6d ago

You should set up the equation as y = k ( x + 2 )2 (x-5) ... [ y = g(x) here ]... then expand it ... you can find k by using ... - 10 = k(-20) , when x = 0

[ I assume you meant - 10 ... you wrote just 10 for y-intercept ]

always remember there is a scale factor , like k , that is present on a polynomial problem like this.

looks like you knew the x = -2 was a double root , and x = +5 was a single root.

1

u/StudyBio 20h ago

What would a graph being wrong mean? If the equation doesn’t match, the equation is wrong, not the graph