Question

Dalyn has been asked to consider the following functions:

f (x) = 6x² - 12x + 11
g (x) = 6(x - 1)² + k


Dalyn would like to find a value of a k such that both f(x) and g(x) model the same graph. Help Dalyn solve for the value of k so both functions will represent the same graph.

Answer 1

In order that both functions to represents the same (one) graph then the value of k is 5

Explanation:

The given functions are;

f(x) = 6·x² - 12·x + 11

g(x) = 6·(x - 1)² + k

Expanding the function g(x) gives;

6·(x - 1)² + k = 6 × (x² - 2·x + 1) + k = 6·x² - 12·x + 6 + k

∴ 6·(x - 1)² + k = 6·x² - 12·x + 6 + k

Comparing with the function for f(x), we have;

f(x) = 6·x² - 12·x + 11

g(x) = 6·(x - 1)² + k = 6·x² - 12·x + 6 + k

The difference between the two functions is the constant term, which are;

Constant term for f(x) = 11

Constant term for g(x) = 6 + k

For the two terms to describe exactly the same graph, the constant term should also be equal

We will then have, 11 = 6 + k

∴ k = 11 - 6 = 5

k = 5

For both functions to represent the same graph the value of k = 5.