Answer:
B, D, and E.
Step-by-step explanation:
We are given the graph:
[tex]f(x)=(x+5)(x-3)[/tex]
We can expand the equation into standard form:
[tex]f(x)=x^2+2x-15[/tex]
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:
[tex]0=(x+5)(x-3)[/tex]
Zero Product Property:
[tex]x+5=0\text{ or } x-3=0[/tex]
Solve:
[tex]x=-5\text{ or } x=3[/tex]
So, our x-intercepts are (-5, 0) and (3, 0).
The y-intercept occurs when x = 0. Hence:
[tex]f(0)=(0+5)(0-3)=-15[/tex]
So the y-intercept is (0, -15).
The axis of symmetry is given by:
[tex]\displaystyle x=-\frac{b}{2a}[/tex]
In this case, from standard form, a = 1, b = 2, and c = -15. Hence:
[tex]\displaystyle x=-\frac{2}{2(1)}=-1[/tex]
Our axis of symmetry is -1.
Therefore, the correct statements are B, D, and E.
