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Which of the following statements are true of the graph of the function f(x)=(x+5)(x-3)? a. The graph has a relative maximum b.The graph has a relative minimum c.The graph has an x intercept at 5,0 d. The graph has an x intercept at 3,0 e. the graph has an y intercept at 0,-15 f. The axis of symmetry is x=-2
Answers: b, d and eb.The graph has a relative minimumd. The graph has an x intercept at 3,0e. the graph has an y intercept at 0,-15 f(x)=(x+5)(x-3)The given equation is in the form of f(x) = a(x-b)(x-c)If ‘a’ is positive then graph has a relative minimumIf ‘a’ is negative then graph has a relative maximumHere a=1 that is positive so graph has a relative minimum .To find x intercept we set f(x) =0 and solve for x0=(x+5)(x-3)x+5 =0 -> x = -5 so x intercept is (-5,0)x – 3=0 -> x= 3 so x intercept is (3,0)To find y intercept we plug in 0 for xy=(x+5)(x-3)y=(0+5)(0-3) = -15so y intercept is (0,-15)
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