Question

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

Answer 1

Answer:

The fourth graph (see attachment)

Step-by-step explanation:

• The function $f(x)=0.03x^2\times{(x^2-25)}$ 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 $0.03x^2\times{(x^2-25)}$=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  $f(x)=0.03(2)^2\times{(2^2-25)}$ , 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.