How do I find an equation of a parabola that has a vertex of

How do I find an equation of a parabola that has a vertex of (-1,0) and focus of (plus/minus5,0)?

Solution

vertex of (-1,0) and focus of (5,0)

distance fromm focus to vertex , a=[(-1-5)²+(0-0)²] =6

general equation of parabola opened to right is (y-k)²=4a(x-h)

vertex (h,k)=(-1,0),a =6

(y-0)²=4*6(x-(-1))

y²=24(x+1)

y²=24x+24

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vertex of (-1,0) and focus of (-5,0)

distance fromm focus to vertex , a=[(-1+5)²+(0-0)²] =4

general equation of parabola opened to left is (y-k)²=-4a(x-h)

vertex (h,k)=(-1,0),a =4

(y-0)²=-4*4(x-(-1))

y²=-16(x+1)

y²=-16x-16