Given:
The equation of a function is

To find:
The graph of the given function.
Solution:
The vertex form of a parabola is
...(i)
Where, (h,k) is vertex of the parabola.
We have,
...(ii)
From (i) and (ii), we get

The vertex of the parabola is (4,1).
Now, the table of values is
x y
2 5
3 2
4 1
5 2
6 5
Plot these points on a coordinate plane and connect them by a free hand curve.
The graph of given function is shown below.
The height of the ceiling is 162.31 meters
The situation will form a right angle triangle.
<h3>Right angle triangle:</h3>
Right triangle has one of its angles as 90 degree. Therefore, the sides can be found using trigonometric ratios
The triangle formed, the theodolite distance from the spotlight is the adjacent side. Therefore,
tan 62.7 = opposite / adjacent
tan 62.7 = x / 83
cross multiply
x = 83 × tan 62.7
x = 160.809554025 m
Therefore, the height of the ceiling form the ground is as follows:
- 160.809554025 + 1.5 = 162.309554025 m
learn more on right angle triangle here; brainly.com/question/13481976
Again, guess and test should work perfectly fine. Since 2(x+y)=32, x+y = 16. Because y-2 =x, y could be = 9 and x = 7. Hope that help!
Answer:
B) y = x + 2 and y = -x - 4
Step-by-step explanation:
Let the equation of a straight line with x-intercept 'a' and y-intercept 'b' be

The line with positive slope has x-intercept a=-2 and y-intercept b=2.
Its equation is:

Multiply through by 2

Solve for y,

For the line with a negative slope,
the x-intercept is a=-4 and the y-intercept is b=-4
Its equation is

Multiply through by -4

Solve for y
