A family of cubic functions have zeros of -2 and 4±7. 4) Write the equation...

Judith McQueen

Judith McQueen

Answered question


A family of cubic functions have zeros of -2 and 4±7.
4) Write the equation ofthe family of cubic Functions in factored form. The equation may contain a ‘non-factorable quadratic but should contain no radicals. Show your work,
b) Write the equation for the member which goes through the point (2, -72). Show vour work,
c) Describe the end behaviour for the member in b).

Answer & Explanation

Ana Robertson

Ana Robertson

Beginner2021-12-08Added 26 answers

Step 1
Family of cubic functions that have the roots a,b and c is y=D(xa)(xb)(xc), here D is a constant.
Given roots are: a=2,b=4+7 and c=47.
(a) y=D(x(2))(x(4+7))(x(47))
Step 2
(b) Substitute x=2 and y=72 o y=D(x+2)(x28x+9) and solve for D.
For cubic equation which goes through point (2, -72) substitute D=6  y=D(x+2)(x28+9)
we get, y=6(x+2)(x28x+9)
The graph y=6(x+2)(x28x+9) shows the cubic equation passing through the point (2, -72) which have
the three roots 2,4+76.646 and 471.354.

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