Answer:
Focus: (-8,-8) Directrix: y=-10
Step-by-step explanation:
1. Rewrite the parabola in standard form:
y=1/4x^2+4x+7
2. Complete the square for the x=terms:
y=1/4(x+8)^2=9
3. Compare to standard equation
y=1/4p(x-h)^2+k, we have y=1/4(x+8)^2-9
Where (h,k) is the vertex of the parabola.
4. Solve for p
1/4p=1/4
p=1
5. Focus
(h, k+p)=(-8, -9+1)=(-8,-8)
Directrix:
1. Consult the formula
y=k-p where k and p are the same terms from above.
y=-9-1=-10
