Need to pass this test to graduate

Mathematics

1 answer:

Paraphin [41]2 years ago

5 0

The 1st graph has vertex in (-3, -3) which can be translated into
Horizontal shift left 3
Vertical shift down 3
Other than that, the graph shows y=x^2 so it wasn't compressed or stretched

The 2nd graph has vertex in (0, 0) which mean there is no vertical and horizontal shift. But the graph is facing down and it was slimmer than y=x^2 graph. When x=1, the result is y=3 which was 3 times more than it supposed to be.
The graph must be:
Reflection across x-axis
Vertical stretch of 3

The 3rd graph has vertex in (3, -3) which can be translated into
Horizontal shift right 3
Vertical shift down 3
Same as the 1st graph, the 3rd graph shows y=x^2 so it wasn't compressed or stretched.

You might be interested in

Give an example of a point that is the same distance from (3, 0) as it is from (7, 0). Find lots of examples. Describe the confi

Artist 52 [7]

Supposse that the distance from the point $(x,y)$ to the point $(3,0)$ is equal to the distance from $(x,y)$ to the point $(7,0)$ . Then, by the formula of the distnace we must have

$\sqrt{(x-3)^2 + (y-0)^2}=\sqrt{(x-7)^2 + (y-0)^2}$

cancel the square root and the $(y-0)^2$ 's, and then expand the parenthesis to obtain

$x^2 - 6x + 9 = x^2 - 14x + 49$

then, simplifying we obtain

$8x = 40$

therfore we must have

$x=5$

this means that the points satisfying the propertie must have first component equal to 5. So we can give a lot of examples of such points: $(5,0), (5,7),(5,1/2), (5,-10),...$ . The set of this points give us a straight line and the points (3,0) and (7,0) are symmetric with respect to this line.