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

Answer:

B, D, and E.

Step-by-step 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:

$\displaystyle x=-\frac{b}{2a}$

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

$\displaystyle x=-\frac{2}{2(1)}=-1$

Our axis of symmetry is -1.

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