X intercept of y=-2(x+3)^2+1

Question

Algebra 2 I also need to find directrix and focus

Answer 1

x-intercept is when y=0:

2(x+3)²=1, x+3=±√½=±√2/2, so the x ints are at (-3-√2/2,0) and (-3+√2/2,0).

The vertex of the parabola is (h,k)=(-3,1) and the focus is at (h,f) where f-k=1/(4a) and a=-2 the coefficient of the squared term. So f-1=-1/8, f=7/8 and the focus is at (-3,7/8).

The directrix line is y=k-(f-k)=1-(7/8-1)=9/8.