which quadratic function has its vertex at (-2,7) and opens down?

Question

a. y= -3(x+2)^2+7
b. y= (x-2)^2+7
c. y= -12(x+2)^2-7
d. y= -2(x-2)^2+7

Answer 1

a. y= -3(x+2)^2+7

Answer 2

a) y=-3(x+2)^2+7

Answer 3

If it opens down, as x becomes a very large positive or negative number, y should be a large negative number.

In a quadratic, with large positive or negative x, the x^2 term will always dominate.
So we look for equations with
y = minus something x^2

a, c, and d fit the bill. b can be eliminated.

now plug in x=-2 and calculate y for each of a, c, and d till we find a y = 7.

for a, y = -3(-2 +2)^2 + 7 = (-3 * 0) + 7 which is what we want.

The answer is a.

Answer 4

y= -(x+2)^2 +7