Question

The function h(x)= x^2+3 and g(x)= x^2-6. If g(x) = h(x) +k, what is the value of k

Answer 1

k = -9

Explanation:

`h(x)=x^2+3\\\\g(x)=x^2-6\\\\g(x)=h(x)+k\qquad(*)\\\\\text{Substitute to (*)}:\\\\x^2-6=x^2+3+k\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\x^2-x^2-6=x^2-x^2+3+k\\\\-6=3+k\qquad\text{subtract 3 from both sides}\\\\-6-3=3-3+k\\\\-9=k\to k=-9`

Answer 2

k = - 9

Explanation:

h(x) = x² + 3

g(x) = x² - 6

g(x) = h(x) + k

x² - 6 = x² + 3 + k

-6 - 3 = k

k = - 9