SOLUTION: a family of quadratic functions has zeros -3 and 5.Which of the following is a member of this family? a) y= -1/2(x+3)(x-5) b) y= 2(x+3)^2(x-5) c) y= 4(x+3)(x-5)(x+15) d) y=(x+5

Question 1068849: a family of quadratic functions has zeros -3 and 5.Which of the following is a member of this family?
a) y= -1/2(x+3)(x-5)
b) y= 2(x+3)^2(x-5)
c) y= 4(x+3)(x-5)(x+15)
d) y=(x+5)(x-3)
draw me a graph with polynomial function of cubic equation with roots -2,3,and 4
what are the real roots of x^4-2x^3+3x+2=0
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Options b) and c) show polynomials of degree 3:
b) y= 2(x+3)^2(x-5) an
c) y= 4(x+3)(x-5)(x+15)
Polynomials of degree 3 can be called "cubic functions,"
but the name "quadratic" is reserved for polynomial of degree 2,
like choices a) and d) :
a) y= -1/2(x+3)(x-5)
d) y=(x+5)(x-3)

If a polynomial function has a as a zero,
its factored form will have the factor .
If a polynomial function has a as a zero,
its factored form will have the factor .
Substituting in a polynomial with as a factor will make the polynomial zero.
Substituting in a polynomial with as a factor will make the polynomial zero.
is
a quadratic function,
and it has and as zeros.

A polynomial is not allowed to have more zeros than its grade.
A polynomial of degree 2,
such as ,
can have at most 2 zeros.
Substituting or in
gives you ,
so obviously the zeros of
are and .
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