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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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(5398) About Me  (Show Source):
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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 5 as a zero,
its factored form will have the factor %28x-5%29 .
If a polynomial function has a -3 as a zero,
its factored form will have the factor %28x-%28-3%29%29=%28x%2B3%29 .
Substituting x=5 in a polynomial with %28x-5%29 as a factor will make the polynomial zero.
Substituting x=-3 in a polynomial with %28x%2B3%29 as a factor will make the polynomial zero.
highlight%28matrix%281%2C2%2C%22a+%29%22%2Cy=+%28-1%2F2%29%28x%2B3%29%28x-5%29%29%29 is
a quadratic function,
and it has -3 and 5 as zeros.

A polynomial is not allowed to have more zeros than its grade.
A polynomial of degree 2,
such as y=%28x%2B5%29%28x-3%29 ,
can have at most 2 zeros.
Substituting x=-5 or x=3 in y=%28x%2B5%29%28x-3%29
gives you y=0 ,
so obviously the zeros of y=%28x%2B5%29%28x-3%29
are 3 and -5 .