Question

Use the graph of f(x) = x2 to write an equation for the function represented by each graph.

Answer 1

Answer:

y = -(x + 2)² + 1

Step-by-step explanation:

Parent function given in the graph is a quadratic function,

f(x) = x²

Since, graph is opening downwards transformed function of the preimage will be,

g(x) = -x²

This transformed function is shifted further by 2 units left horizontally and 1 unit upwards.

Therefore, rule for the transformation will be,

g(x) → h[(x + 2), (y + 1)]

By this rule transformed function will be,

h(x) = -(x + 2)²+ 1

Equation of the curve will be,

y = -(x + 2)² + 1