Question

The vertex of the parabola in the xy-plane above is (0,C) . Which of the following is true about the parabola with the equation y= -a(x-b)^2+C?


a- The vertex is (b,c) and the graph opens upward.
b- The vertex is (b,c) and the graph opens downward.
c- The vertex is (-b,c) and the graph opens upward.
d- The vertex is (-b,c) and the graph opens downward.

Answer 1

Here are the basic rules that may help you:
-When the coefficient of a is negetive, the parabola will open downwards, but if it is positive, it will open normal (upwards)
-The closer a is to zero, the wider. Fractions are wider parabolas and whole numbers are skinner parabolas
- (x-b) is the natural state. That means if it is minus b, it goes to the right, because b is positive, and if it plus b, it goes to the left because b is negetive. Think about the x axis and moving right and left.
- C is naturally added. That means if c is added, the graph goes up, and if c is subtracted, the parabola goes down. Think about the y axis moving up/down.

Based on these rules, the vertex of the equation would be (b, c) and it would open down. Hope this helped!

Answer 2

Nice presentation! @asc.bchs