Let fx x2 10x 27 Find the vertex Answer State the range of

Let f(x) = x^2 + 10x+ 27. Find the vertex. Answer: State the range of the function. Answer: On what interval is the function decreasing? Answer: Consider the polynomial P(x), shown in both standard form and factored form. Which sketch illustrates the end behavior of the polynomial function? Answer: State the zeros of the function. State the y-intercept State which graph below is the graph of P(x).

Solution

19)

f(x)=x^2 +10x +27

f(x)=(x^2 +10x) +27

f(x)=(x^2 +10x+25-25) +27

f(x)=(x^2 +10x+25)-25 +27

f(x)=(x^2 +10x+25)+2

f(x)=(x+5)^2 +2

f(x)=(x-(-5))^2 +2

vertex of y =(x-h)^2 +k is (h,k)

vertex =(-5,2)

range is (2,infinity)

function is decreasing in interval (-infinity,-5)