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50Pts guys!!!! Please help me its easy!

The equation of a quartic function f(x) with zeros -2,0,1,4 and such that f(x) → ∞ as x -∞, is

Select one:

a. f(x) = x(x-2)(x+1)(x+4)

b. f(x) = -x(x-2)(x+1)(x+4)

c. f(x) = x(x+2)(x-1)(x-4)

d. f(x) = -x(x+2)(x-1)(x-4)

User Belugabob
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1 Answer

21 votes
21 votes

Answer:

c. f(x)=x(x+2)(x-1)(x-4)

Explanation:

Where it says "as x goes to negative infinity" then "y goes to infinity" (that's the part with the infinity symbols) that means the graph is going up at it's left end. This curve is a quartic (4th degree) which means its left and right ends are kind of parabola-ish, but the middle is not the neat u-ish, v-ish shape of a parabola; it's more like a wonky, noodle-ish wavy affair. Anyway, LIKE a parabola when the beginning of the equation is positive, the two ends point up. That's what's happening here and so we can eliminate b. and d. as potential answers.

Since -2, 0, 1, 4 are zeros (which are solutions...and also x-intercepts) we can find the factors of the function.

If x = -2

ADD 2 to both sides.

x + 2 = 0

This means (x+2) is a factor.

This is enough info to select answer c. but let's verify the other factors.

If x = 1

SUBTRACT 1 from both sides.

x - 1 = 0

Thus means (x - 1) is a factor.

If x = 4

SUBTRACT 4 from both sides.

x - 4 = 0

(x - 4) is a factor.

You can see c. has all these factors as well as x, because x=0 already, so x is a factor too.

I think of this as a working backwards problem, bc usually you have to factor and solve. This one, you have solutions (which are zeros and x-intercepts) and work backwards to find factors and multiply them together to find the function.

User Drwowe
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