Write the quadratic function in f(x)= a(x-h)^2+k form whose graph is shown.

f(x)=

f(x) = - (x - 2)² + 2

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

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

Here (h, k) = (2, 2 ), thus

y = a(x - 2)² + 2

To find a substitute the point (0, - 2) into the equation

- 2 = a(- 2)² + 2 ( subtract 2 from both sides )

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

a = - 1

Thus

f(x) = - (x - 2)² + 2

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

it would rotate about 180 degrees.