Answer:
B, D, and E.
Step-by-step explanation:
We are given the graph:
![f(x)=(x+5)(x-3)](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B5%29%28x-3%29)
We can expand the equation into standard form:
![f(x)=x^2+2x-15](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2%2B2x-15)
Since the leading coefficient is positive, our parabola curves up. Hence, it has a relative minimum.
The <em>x-</em>intercepts of a function is whenever <em>y</em> = 0. Hence:
![0=(x+5)(x-3)](https://tex.z-dn.net/?f=0%3D%28x%2B5%29%28x-3%29)
Zero Product Property:
![x+5=0\text{ or } x-3=0](https://tex.z-dn.net/?f=x%2B5%3D0%5Ctext%7B%20or%20%7D%20x-3%3D0)
Solve:
![x=-5\text{ or } x=3](https://tex.z-dn.net/?f=x%3D-5%5Ctext%7B%20or%20%7D%20x%3D3)
So, our <em>x-</em>intercepts are (-5, 0) and (3, 0).
The <em>y-</em>intercept occurs when <em>x</em> = 0. Hence:
![f(0)=(0+5)(0-3)=-15](https://tex.z-dn.net/?f=f%280%29%3D%280%2B5%29%280-3%29%3D-15)
So the <em>y-</em>intercept is (0, -15).
The axis of symmetry is given by:
![\displaystyle x=-\frac{b}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D-%5Cfrac%7Bb%7D%7B2a%7D)
In this case, from standard form, <em>a</em> = 1, <em>b</em> = 2, and <em>c</em> = -15. Hence:
![\displaystyle x=-\frac{2}{2(1)}=-1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D-%5Cfrac%7B2%7D%7B2%281%29%7D%3D-1)
Our axis of symmetry is -1.
Therefore, the correct statements are B, D, and E.