Question

Sketch the graph y=−|x−1|+3 and answer the questions:
Does it open upward?
Yes or No?

Answer 1

1) Please see the required graph created with Microsoft Excel

2) No

Explanation:

The given parameters are;

`y= -\left | x - 1 \right | + 3`

From the given equation, we have;

When x > 4, or x -2 <, y < 0, which gives;

y > 0 for -2 < x < 4

Therefore, the graph is opened in the downward direction with the peak at the point with coordinate (1, 3)

The legs of the graphs are straight lines with slopes = -1, and 1 respectively, before and after the maximum point of the graph

The table of values used to sketch the graph with Microsoft Excel is given as follows;

x
`{}` y

-3 -1

-2 0

-1 1

0 2

1 3

2 2

3 1

4 0

5 -1