In the xy-plane, the parabola with equation y=-x^2+4 has its vertex at point C and intersects the x-axis at two points, A and B. What is the area of triangle ABC?




Comments (3)

There are a few shortcuts to remember about parabola equations, two of which are helpful here.

1) When a parabola is in y = ax^2 + bx + c form, c tells you the y-intercept.

2) When a parabola is in the same y = ax^2 + bx + c form and b = 0 as it does here, the parabola is centered (i.e., has its vertex) on the y-axis.

I was able to figure the downward parabola and vertex (0, 4) at first glance but how can we also be able to recognize that the parabola will only travel left or right 2 units before it travels down 4 units to the x-axis. This makes it a lot faster to understand conceptually. Thanks!

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