Question

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5). Write the equation of this cubic polynomial function. Recall that the zeroes are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?
–5
–2
3
5

Answer 1

Answer:

Equation of the polynomial function is

$f(x)=\frac{1}{6}( x^3-10x^2+31x-30)$

The y-intercept is -5

Step-by-step explanation:

According to the Descarte's theorem , a polynomial p(x) that has a zero r, that is p(r)=0, then it follows (x-r) is a factor of p.

If f(x) has zeros 2,3 and 5 then f(x) has factors (x-2),(x-3) and (x-5) hence to find the equation

f(x)=a(x-2)(x-3)(x-5)

f(x)={a(x-2)(x-3)(x-5)}-----------------------expand

f(x)={a (x(x-3)-2(x-3)⇒x²-3x-2x+6⇒x²-5x+6

f(x)={a (x²-5x+6)(x-5)}

f(x)={a x(x²-5x+6)-5(x²-5x+6)}

f(x)=a(x³-5x²+6x-5x²+25x-30)

Given that we have one hang point (0,-5), let x=0, f(x)=-5 find a

-5=a(0-0+0-30)

-5=-30a

a=-5/-30

a=1/6

Equation⇒ f(x)=1/6 (x³-10x²+31x-30)

To get y-intercept plugin x=0 in the equation , you notice the value of the function will be -5, hence y-intercept is -5

Answer 2

Answer:

A) -5

Answer to the 2nd question: the linear factors of the cubic are: A) (x-2)(x-3)(x-5)

Answer to the 3rd question: to solve for the leading coefficient, use: D) -5=a(0-2)(0-3)(0-5)

Answer to the 4th question: A=1/6

Answer to the 5th question: write the function: f(x)=1/6  x^3-=5/3 x^2+=31/6 x-=5