Question

The graph of h is the graph of g(x)=(x-2)^2+6 translated 5 units left and 3 unit downa. Describe the graph of h as a translation of the graph of f(x)=x^2b. Write the function h in vertex form

Answer 1

The function, g(x) is given as

g(x) = (x - 2)^2 + 6

If a function, f(x) is translated c units to the left, it becomes

f(x + c)

Thus, if we translate g(x) 5 units to the left, it becomes

h(x) = (x - 2 + 5)^2 + 6

h(x) = (x + 3)^2 + 6

If we translate a function, f(x) c units down, it becomes

f(x) - c

Thus, if we translate h(x) = (x + 3)^2 + 6, 3 units down, it becomes

h(x) = (x + 3)^2 + 6 - 3

h(x) = (x + 3)^2 + 3

a) For h(x) = (x + 3)^2 + 3 to become f(x) = x^2, it means that h(x) would be written like this

h(x) = (x + 3 - 3)^2 + 3 - 3

This means that the graph of h(x) was translated 3 units right and 3 units down.

B) The vertex form of a quadratic function is expressed as

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

Comparing with h(x) = (x + 3)^2 + 3,

The vertex form of h(x) is

h(x) = (x + 3)^2 + 3