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:

Answer is D

Step-by-step 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.

Step-by-step 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.