Question

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

Answer 1

the answers would be
b
d
e

Answer 2

Answers: b, d and e

b.The graph has a relative minimum

d. The graph has an x intercept at 3,0

e. 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 minimum

If 'a' is negative then graph has a relative maximum

Here a=1 that is positive so graph has a relative minimum .

To find x intercept we set f(x) =0 and solve for x

0=(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 x

y=(x+5)(x-3)

y=(0+5)(0-3) = -15

so y intercept is (0,-15)