SOLUTION: Using y2 -4y -4x = 0, Find the vertex, the focus, and the directrix then graph the equation

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Question 1073151: Using y2 -4y -4x = 0, Find the vertex, the focus, and the directrix then graph the equation
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
y%5E2-4y-4x=0
4x=y%5E2-4y
4x=y%5E2-4y%2B4-4
4x=%28y-2%29%5E2-4
4x%2B4=%28y-2%29%5E2
highlight%284%28x%2B1%29=%28y-2%29%5E2%29

Vertex is the left-most point, and the parabola opens toward the right. Symmetry axis is parallel to the x-axis.

Equation indicates vertex (-1,2).

The factor 4 on the left indicates that some distance p so that 4p=4, is how far both the directrix and focus are from the vertex. Here, p=1.

DIRECTRIX: x=-2
FOCUS: (0,2)


graph%28300%2C300%2C-2%2C8%2C-3%2C7%2C2-2sqrt%28x%2B1%29%2C2%2B2sqrt%28x%2B1%29%29