Question

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

Answer 1

Answer:

1) Please see the required graph created with Microsoft Excel

2) No

Step-by-step 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