What is the answer for number 3a,b and 4? 3. This problem concerns the polynonia

Question

What is the answer for number 3a,b and 4? 3. This problem concerns the polynonia|nction,(x) =-2ra + B' a. Does this function have yas symmetry, origin symmetry, or neither? How can you tell without looking at the graph? b. Find the Kintercepts State whether the graph orosses the w-axis, or touches the w-axis and tuns around, at each intercept. Explain how you can tell without looking at the graph Give an example of one polynomial function with arthese features below. Tom ake grade, give your answer in factored form easy for me to . The end behavior is the same as the end behavior of- There are only two zeros: 7 and -1 The graph crosses the x-axis at-1 The graph touches the -axis at -7 and tures around Page 1 3

Explanation / Answer

3
f(x) = -2x^2 + 4x^4
a> the function f(x) shows origin symmetry we could see this by observing the fact that the function f(x)
is an even function . and even functions are symmetric to the y axis.
A function f(x) is an even function if on replacing x by -x we get the same function .

that is f(-x) = f(x) , then f(x) is an even function.

f(x) = -2x^2 + 4x^4
=> f(-x) = -2(-x)^2 + 4(-x)^4 = -2x^2 + 4x^4

since f(-x)= f(x)
So, the function f(x) shows y axis symmetry.

b> we'll get the x intercepts by solving the equation f(x) = 0 for x

at the x intercepts the y or the f(x) values are 0

=> -2x^2 + 4x^4 = 0
-2x^2[1 - 2x^2] = 0

x= 0 , 1-2x^2 = 0 = > x = +-1/sqrt(2)

hence the x intercepts are x = 0 ,x = 1/sqrt(2) and x =-1/sqrt(2)

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