Please help me out with this equation!
i will mark as brainliest

 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

the correct functions are

h(x) = 3x + 2  

g(x) = 2^x

step-by-step explanation:

i proceed to calculate the different values ​​of k (x)

case 1)  k(x) = g(x) ∘ h(x)

g(x) ∘ h(x)=g(h(x))

k(x) = [2]^[3x + > is the option  4. k(x) = 2^(3x + 2 )

case 2)  k(x) = g(x) + h(x)

k(x) = [2^x]+[3x + 2]=2^x+3x+> is the option  1.) k(x) = 2^x + 3x + 2

case 3)k(x) = h(x) ÷ g(x)

k(x) =  [3x + 2]/[2^x]=3x/(2^x)+2/(2^x)=3x*(2^-x)+2^(1-x)

is the option  3.)   k(x) = (3x)2^(-x) + 2^(-x + 1 )

case 4)k(x) = g(x) - h(x)

k(x) =  [2^x]-[3x + 2]=2^x-3x-> is the option  2.) k(x) = 2^x - 3x - 2 

case 5)  k(x) = g(x) × h(x)

k(x) = [2^x]*[3x + > is the option  5.) k(x) = 2^x(3x + 2)

case 6)k(x) = h(x) ∘ g(x)

h(x) ∘ g(x)=h(g(x))

k(x)=3*[2^x]+> is the option  6. k(x) = 3(2^x) +2

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11