What does the graph of y = (x + 2)(x + 1)(x – 3)2 do near the point (3, 0)?The graph is the x-axis to its left, then , and is the x-axis to its right.

Accepted Solution

Answer:(3,0) the graph touches the x-axisStep-by-step explanation:the graph of [tex]y = (x + 2)(x + 1)(x – 3)^2[/tex]we need to check what happens to the graph near the point (3,0)In f(x) we have (x-3)^2 LEts plug in 3 for x and check[tex]y = (3 + 2)(3 + 1)(3 – 3)^2[/tex]y=0, so (3,0) is one of the zero of the given f(x)In f(x) we have [tex](x-3)^2[/tex]Exponent is 2 that is even. It means the multiplicity is even. When the multiplicity is even then the graph touches the x axis but does not cross x axisSo at (3,0) the graph touches the x-axis