Find the axis of symmetry and what direction the parabola opens. -1/4(y+4)=(x-3)²

2 answers
Question:

Find the axis of symmetry and what direction the parabola opens.
-1/4(y+4)=(x-3)²

Answers

First, convert the equation to the standard equation of a parabola.-1/4(y+4)=(x-3)^2     ---multiply -4 on both sides   y+4=-4(x-3)^2           ---subtract 4 on both sidesy=-4(x-3)^2-4From the equation, we know that the parabola was moved by 3 to the right, because of (x-3)^2. So the axis of symmetry is x=3. Now look at the number in front of (x-3)^2. It is -4. Since it is negative, the parabola opens downwards. 

Equation of parabola ==> (y-k) = a(x-h)²To find te direction of this parabola, multiply both sides by (-1) ==>1/4(y+4) - (x+3)². Since "a" is negative, the parabola opens downward & hence it's Vertex is a MAXIMUM.Let's calculate this Maximum:Vertex (h , k) and Axis of symmetry x=hThe given function: -1/4(y+4)=(x-3)², where k=- 4 & h= +3Hence the axis of symmetry is x=3 & the vertex is at (3, -4)

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