Write a formula for quadratic function if its graph has the vertex at point ( 1/3 ,−3) and passes through the point (1,1).

f(x) = 9(x -1/3)^2 -3

Step-by-step explanation:

In vertex form the equation of a quadratic with vertical scale factor "a" and vertex (h, k) is ...

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

To make the equation have (1, 1) as a solution, we need to find the value of "a". We can put the point coordinates in the equation and solve for "a":

1 = a(1 -1/3)^2 -3 . . . . . for (h, k) = (1/3, -3) as given

1 = (4/9)a -3 . . . . simplify

4 = (4/9)a . . . . . . add 3

9 = a . . . . . . . . . . multiply by 9/4

The quadratic function you desire is ...

f(x) = 9(x -1/3)^2 -3

required rate of return = 0.166 = 16.6%

step-by-step explanation:

under the capital asset pricing model (capm), the required or expected rate of return for a particular security or asset is given using the formula:

required rate of return = risk-free rate + beta*(market risk premium)

we are given that;

risk-free rate = 4% = 0.04

beta = 1.4

market risk premium = 9% = 0.09

we simply plug these values into the above formula;

required rate of return = 0.04 + 1.4*(0.09)

required rate of return = 0.04 + 0.126

required rate of return = 0.166 = 16.6%