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

The equation for the function represented by the graph is and this can be determined by using the transformation.

Given :

The following steps can be used to determine the equation represented by the given graph:

Step 1 - The given graph is concave downwards that means it is a reflection of the function . So, the function becomes .

Step 2 - The given graph is shifted horizontally in the left direction by 2 units. So, the above function now becomes:

Step 3 - The given graph is shifted vertically upwards in the positive y-axis direction by 1 unit. So, the above function now becomes:

So, the final equation for the function represented by the graph is .

For more information, refer to the link given below:

link

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

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