John can service a television and a cable box in one hour. It took him four hours yesterday to service two televisions and ten c
1 answer:
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Answer:
<em>Vertex: (3,4)</em>
Step-by-step explanation:
<u>Vertex form of the quadratic equation</u>
The vertex form of the quadratic function has the following equation:
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
The parabola is given as:
Comparing with the equation:
a=2, Vertex: (3,4)
The graph of the parabola is shown in the image below
Given:
The system of inequalities:
To find:
The point that represents a solution to the system by using the graph.
Solution:
We have,
The related equations of these inequalities are:
The line is a vertical line that intersect the x-axis at 3.
The table of values for is:
x y
0 -5
1 -3
Plot (0,-5) and (1,-3) on a coordinate plan and connect them by a straight line.
The boundary lines are dotted lines because the points on the lines are not included in the solution set.
Check the inequalities for (0,0).
First inequality: ( False)
Second inequality:
(False)
Both inequalities are false for (0,0). It means the shaded region of the lines is in the opposite direction of (0,0).
Plot the shaded region and the points (-3, -1), (1, 11), (4, -1), (5, 6) as shown in the below graph.
From the below graph, it is clear that the point (4,-1) is the only point lies in the common shaded region. So, (4,-1) represents a solution to the system.
Therefore, the correct option is C.
