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Which of the following graphs could be the graph of the function


f(x)=0.03x^2(x^2-25)

Which of the following graphs could be the graph of the function f(x)=0.03x^2(x^2-25)-example-1
Which of the following graphs could be the graph of the function f(x)=0.03x^2(x^2-25)-example-1
Which of the following graphs could be the graph of the function f(x)=0.03x^2(x^2-25)-example-2
Which of the following graphs could be the graph of the function f(x)=0.03x^2(x^2-25)-example-3
Which of the following graphs could be the graph of the function f(x)=0.03x^2(x^2-25)-example-4
User P Daddy
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8.1k points

2 Answers

2 votes
The answer to this problem which is the correct graph is the "FIRST graph". We have the given function:

f(x) = 0.03x² (x²-25)

From our evaluation, the has a power of "4".
When we try to start plotting points, we can check if the is reflecting these points.

First point is when x=1,
y=0.03x²(x²-24)
y =-0.72

The second point is when x= 6
y=0.03*6² *(6²-24)
y= 12.96

Only the FIRST graph satisfies these points.
User Kevlarkevin
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8.3k points
2 votes

The given function is


f(x) = 0.03x^2 (x^2-25)

To check out the graph, first we have to find the zeroes and there multiplicities .

TO find the zero, we put 0 for f(x), and solve for x, that is


0.03x^2(x-5)(x+5)=0 \\ 0.03x^2 =0, x-5=0, x+5=0 \\ x=0 \ multiplicity \ 2, x=5 \ multiplicity \ 1, x=-5 \ multiplicity \ 1

With odd multiplicity, the graph crosses the x axis and for even multiplicity, the graph takes a u turn at the zero .

So the correct graph is represented by first option .

User Bierbarbar
by
7.7k points