Question

The graph of y=x^2 is shown below. which of the following could be the graph of y=x^2-3

first pic is original graph, next are options A, B, C, and D

Answer 1

Answer is D

Explanation:

Given the graph of the function
`y=x^2`

We have to find the new graph
`y=x^2-3`

We find that the new graph is nothing but the transformation of the original graph by a vertical shift of 3 units down.

Reason: Instead of
`y=x^2` we have
`y+3=x^2`

Hence there is a vertical shift down by 3 units and no horizontal change.

Hence the new vertex = (0,-3)

The answer is Graph D

Answer 2

The graph is given below.

Explanation:

We need to find graph of y = x² - 3

At x = 0 we have

y = 0² - 3 = -3

So (0,-3) is a point on the graph.

When y = 0

0 = x² - 3

x = 1.732 and -1.732

So, (1.732,0) and (-1.732,0) are the points on the curve.

All these points are satisfied by the graph given below.