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 (4)

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!

It doesn’t travel left or right 2 units before traveling down 4 units because of the neg in front of the equation tells you that is a sad face, St Louis Mi or a Mcdonalds Arch( all depressing and negative) so that means it travels down 4 before it goes to the right( positive)2 and to the left ( negative ) 2.

its almost like they give you the answers because they say it intercepts x at 2 points a and b — right away you know that a and b are simply the x intercepts which can always be found when y= 0, y = 0 when
– (x^2)+4 =0 or 4 = x^2 and that is +/- 2
right away you see that perfect square and since squares are positive whether the root is negative or positive you can know that -2 and +2 will give you your a and b or x intercepts

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