Please help me out with this equation!
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 Choice D

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

Explanation:

The highest point is (2, 7) so this is the vertex.

In general, the vertex is (h, k). We can say that h = 2 and k = 7.

The vertex form

y = a(x-h)^2 + k

updates to

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

Note that the graph goes through (0,3) which is the y intercept. Plug those x,y coordinates into the equation above to solve for 'a'

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

3 = a(0-2)^2 + 7

3 = a(-2)^2 + 7

3 = a(4) + 7

3 = 4a + 7

4a+7 = 3

4a = 3-7

4a = -4

a = -4/4

a = -1

Therefore, we have

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

update to

y = -1(x-2)^2 + 7

which is the same as

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

and that's why the answer is choice D

D

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k ) = (2, 7 ) , then

f(x) = a(x - 2)² + 7

To find a substitute any point on the graph into the equation

Using (0, 3 ) , then

3 = a(0 - 2)² + 7 ( subtract 7 from both sides )

- 4 = 4a ( divide both sides by 4 )

- 1 = a

f(x) = - (x - 2)² + 7 → D

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