Question

state the solution set using interval notation and sketch its graph of x²+6x+9>0​

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Asked on December 26, 2019 by

Likhitha Shiwankar

Draw the graph of the polynomial f(x)=x

2

−6x+9.

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ANSWER

SOLUTION Let y = f(x) or, y=x

2

−6x+9.

The following table gives the values of y or f (x) for various values of x.

x -2 -1 0 1 2 3 4 5 6 7 8

y=x

2

−6x+9 25 16 9 4 1 0 1 4 9 16 25

Thus, the graph of y=x

2

−6x+9 passes through the points (-2,25), (-1,16), (0,9), (1,4), (2,1),(3,0),(4,1),(5,4),(6,9),(7,16)and (8,25).Let us plot these points on the graph and draw a free hand smooth curve passing through these points. We observe that the vertex of the parabola is at point P (3,0) as shown in Figure.