Question

The graph shows g(x), which is a translation of f(x)=x2. Write the function rule for g(x).

Write your answer in the form a(x–h)2+k, where a, h, and k are integers or simplified fractions.

Answer 1

y = (x + 3)² + 7

Explanation:

the equation of a parabola in vertex form is

y = a(x - h)² + k

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

From the graph

the vertex ( turning point ) = (- 3, 7 ) , then

y = a(x - (- 3) )² + 7 , that is

y = a(x + 3)² + 7

to find a , substitute the coordinates of any other point on the graph into the equation.

using the point (- 2, 8 )

8 = a(- 2 + 3)² + 7 ( subtract 7 from both sides )

1 = a(1)² = a

y = (x + 3)² + 7 ← equation of graph