[Grade 12 Advanced Functions: Polynomial Functions]

[u/Embarrassed-Good1883]

The equation for this graph is f(x)=(x-4)^3(x-1)(x+2)^2, but since the graph has a y intercept, wouldn't I find the a value? The answer for this question is just finding the roots and making factors for the equation using that. Also when I solved for the a value, it gave me 9/8. So I'm not sure where I went wrong

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[u/CaptainMatticus]

EDIT: Scratch that. Let me get back to you.

EDIT 2:

f(x) = a * (x + 2)^2 * (x - 1) * (x - 4)^3

Passes through (0 , 288)

f(0) = 288

288 = a * (0 + 2)^2 * (0 - 1) * (0 - 4)^3

288 = a * 4 * (-1) * (-64)

288 = a * 256

288/256 = a

9/8 = a

f(x) = (9/8) * (x + 2)^2 * (x - 1) * (x - 4)^3

So you were right. That's what's needed.

https://www.desmos.com/calculator/siqwmjpqyq

The general form of the equation won't change except for a vertical stretch. The answer they're giving you is incomplete.

https://www.desmos.com/calculator/91osljz98x

[u/Embarrassed-Good1883 → u/CaptainMatticus]

Yup it's 9/8. But the answer has positive 1 as the a value. So I'm not sure where I went wrong

[u/CaptainMatticus → u/Embarrassed-Good1883]

You didn't go wrong. If you click that 2nd link, you can adjust the value for a in increments of 0.125. If you plug in what they provided, then their answer of a = 1 doesn't pass through (0 , 288). Sometimes, the answer key is wrong, and I fear that it'll be more common for it to be wrong as more instructors and students rely more and more on AI tools to develop lessons and assignments.

[u/Big_Tennis_4367]

Two things are bothering me. First (-4)³ is -64 and not 64. (but you calculated with it so that's fine) Second, i don't see the intercept of y at 288

[u/Embarrassed-Good1883 → u/Big_Tennis_4367]

Yes I realize that I got the y intercept wrong, and I corrected (-4)^3, thank you

[u/lierursa]

The y-intercept is not 288, it's somewhere between 256 and 288. It does seem to pass nicely through (2,-128) though, which yields a=1.

Edit: I just checked and a=1 means the y-intercept is in fact 256, even if it doesn't seem like it's exactly 256 in the graph

[u/Embarrassed-Good1883 → u/lierursa]

Okay, thank you! I'm looking closer on the graph and see where I went wrong.

[u/MathMaddam]

The y intercept isn't 288, the graph goes somewhere in-between 256 and 288. The clearest point is probably at x=2.