For 3x^2 + 72 = −72y, please identify the vertex, focus, axis of symmetry, and directrix. Finally sketch the graph.

Answer 1

Convert of Vertex-form.

Answer 2

-72y = 3x^2 +72

y = -3x^2/72 -1

y =-x^2/24 - 1 or y=(-1/24)(x-0)^2 -1 is the parabola's equation in vertex form

It's a standard parabola compressed or shrunk by a factor of -1/24

vertex is (0, -1)

the parabola is downward opening with axis of symmetry x=0, the same as the x coordinate of the vertex.

the parabola is below the x axis with no x intercepts. The y intercept is the vertex (0,-1)

focus and directrix are equidistant vertically from the vertex (0, -1). each a distance of 6. The focus is below the vertex. The directrix is above the vertex.

The focus is (0, -7) The directrix is y= 5