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Which equation choice could represent the graph shown below?

 

 Mar 24, 2021
 #1
avatar+291 
+1

The zeroes of the polynomial are -4 and 7, which means that the bottom 2 solutions are not correct.

Now, look at the x values of the polynomial in between -4 and 7, and evaluate them at each of the 2 possible solutions. The top right one suggests that the graph is negative between -4 and 7, which is not true, so the top-left answer f(x) = (x+4)(x-7)^2 is the correct answer.

 Mar 24, 2021
 #2
avatar+117787 
+1

To add to what textot said....notice  that  the  graph "cuts"  the  x axis  at  x  = -4   but  it " kisses" the  x axis at  x = 7

 

A graph cutiing the x axis  will  always have an odd multiplicity root  at that point, but a graph "kissing" the x axis will have an even multiplicity root  at  that point

 

Thus......f(x) = (x + 4) ( x - 7)^2  is the only possibility

 

cool cool cool

 Mar 24, 2021

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