Answer:
16. B
17. B
Step-by-step explanation:
16. The intercept form of the parabola is
[tex]y=a(x-x_1)(x-x_2),[/tex]
where [tex]x_1, x_2[/tex] are two x-intercepts.
In your case,
[tex]x_1=2\\ \\x_2=-8[/tex]
so
[tex]y=a(x-2)(x-(-8))\\ \\y=a(x-2)(x+8)[/tex]
To find a, substitute coordinates of the point (-6,-4) parabola is passing through
[tex]-4=a(-6-2)(-6+8)\\ \\-4=-16a\\ \\a=\dfrac{1}{4}[/tex]
and
[tex]y=\dfrac{1}{4}(x-2)(x+8)[/tex]
17. The vertex form of the parabola equation is
[tex]-2p(y-k)=(x-h)^2,[/tex]
where (h,k) are the coordinates of the vertex and sign "-" because parabola goes down.
In your case, vertex is (2,3), so
[tex]-2p(y-3)=(x-2)^2[/tex]
The vertex is 3 units from the focus, then
[tex]\dfrac{p}{2}=3\\ \\p=6[/tex]
The equation of the parabola is
[tex]-2\cdot 6(y-3)=(x-2)^2\\ \\y=-\dfrac{1}{12}(x-3)^2+3[/tex]
