Question

focus(-4,-4); opens left; contains (-7,0)
write the equation for the parabola given set characteristic

Answer 1

Any idea?

Answer 2

The standard form of a left/right open parabola is
\((y -k)^2=4p(x-h)\) where vertex (h, k) and focus (h+p, k)

Answer 3

You have focus (-4,-4) it means h+p= -4 and k =-4
Now, the parabola passes through the point (-7,0) , just replace x=-7 , y =0, k =-4 into the standard form, you have
\((0-(-4))^2=4p(-7-h)\)
accompany with \(h+p =-4\)

Answer 4

You have 2 equations, 2 unknowns h, p--> solveable,
hence: solve for h, p, then plug them back to standard form of parabola and you are done