Question

Which of the following statments are true of the graph of the function f(x) = (x + 5)(x - 3). Select all that apply. pleaseee help this is due tonight!

A. The graph has a relative maximum

B. The graph has a relative minimum

C. The graph has a x-intercept at (5, 0)

D. The graph has a x-intercept at (3, 0)

E. The graph has a y-intercept at (0, -15)

F. The axis of symmetry is x = -2​

Answer 1

B, D, and E.

Explanation:

We are given the graph:

`f(x)=(x+5)(x-3)`

We can expand the equation into standard form:

`f(x)=x^2+2x-15`

Since the leading coefficient is positive, our parabola curves up. Hence, it has a relative minimum.

The x-intercepts of a function is whenever y = 0. Hence:

`0=(x+5)(x-3)`

Zero Product Property:

`x+5=0\text{ or } x-3=0`

Solve:

`x=-5\text{ or } x=3`

So, our x-intercepts are (-5, 0) and (3, 0).

The y-intercept occurs when x = 0. Hence:

`f(0)=(0+5)(0-3)=-15`

So the y-intercept is (0, -15).

The axis of symmetry is given by:

`\displaystyle x=-(b)/(2a)`

In this case, from standard form, a = 1, b = 2, and c = -15. Hence:

`\displaystyle x=-(2)/(2(1))=-1`

Our axis of symmetry is -1.

Therefore, the correct statements are B, D, and E.