Question

Which of the following graphs could be the graph of the function f(x)=0.03x2(x2-25)?

Answer 1

The first graph (A)

Explanation:

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Answer 2

The fourth graph (see attachment)

Explanation:

• The function
  `f(x)=0.03x^2*{(x^2-25)}` represents a polinomial of grade 4, which means that it has four roots. The roots of a function are those values that make the function equal to zero.
• In this particular case, the function f(x) equals zero
  `0.03x^2*{(x^2-25)}\\`=0 in two cases: 1) When the term
  `0.03x^2=0`, which only happens if x=0; or 2) when
  `(x^2-25)=0`, which can happend if x=5 or if x=-5 (because the product of two negative numbers is possitive).
• Then, the function graph must show that, f(x) passes trough zero when x=0 (first case) or when x=5 or x=-5 (second case).The only graph that shows that is the one indicated.
• To verify that the function is well depicted, you can replace any specific value of x (for example x=2) in the equation
  `f(x)=0.03(2)^2*{(2^2-25)}` , an see if the graph shows the correct value of f(x) given x, that in this case it is goint to be f(2)=-2.57.