Question

Find the formula for the cubic function (third degree polynomial) whose graph has the given properties: • A y-intercept of 63 and x-intercepts at x = −8, 25, 30.

Answer 1

We know that the equation of a cubic polynomial having x intercepts(zeros) as a, b, c and leading coefficient as k is given by:-

p(x)=k(x-a)(x-b)(x-c)

Here, a=-8, b=25, c=30

Hence the function will be:

p(x)=k(x-(-8))(x-25)(x-30)

=>p(x)=k(x+8)(x-25)(x-30)

Also it is given that y intercept is 63

=>(0,63) must satisfy p(x)

=>63=k(0+8)(0-25)(0-30)

=>63=k(8)(-25)(-30)

Hence the cubic function is:

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