Answer:
A) [tex]f(x)=0.2(x+2)(x-5)[/tex]
Step-by-step explanation:
The graph has x-intercepts at [tex]x=5[/tex] and [tex]x=-2[/tex], so our factors for the polynomial will be [tex]x+2[/tex] and [tex]x-5[/tex]. This means we can rule out options B and D.
Our graph also has a y-intercept of [tex]y=-2[/tex] when [tex]x=0[/tex], so if we let [tex]f(x)=-2[/tex] and [tex]x=0[/tex], we can find the multiplier:
[tex]f(x)=a(x+2)(x-5)\\-2=a(0+2)(0-5)\\-2=a(2)(-5)\\-2=-10a\\\frac{1}{5}=a\\0.2=a[/tex]
Thus, the correct equation is A) [tex]f(x)=0.2(x+2)(x-5)[/tex]
