How do you graph this ?
1 answer:
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You could complete the square to state the vertex.
You could use the quadratic equation to find the roots (which are complex).
Try an example that will require both.
y = x^2 + 2x + 5
Step One
Get the graph. That's included below.
Step Two
Provide the steps for completing the square.
Note: we should get (-1,4)
y= (x^2 +2x ) + 5
y = (x^2 +2x + 1) + 5 - 1
y = (x +1)^2 + 4
The vertex is at (-1,4)
Step Three
Find the roots. Use the quadratic equation. Note that the graph shows us that the equation never crosses or touches the x axis. The roots are complex.
a = 1
b = 2
c = 5
x = -1 +/- 2i
x1 = -1 + 2i
x2 = -1 - 2i And we are done.
You could use the quadratic equation to find the roots (which are complex).
Try an example that will require both.
y = x^2 + 2x + 5
Step One
Get the graph. That's included below.
Step Two
Provide the steps for completing the square.
Note: we should get (-1,4)
y= (x^2 +2x ) + 5
y = (x^2 +2x + 1) + 5 - 1
y = (x +1)^2 + 4
The vertex is at (-1,4)
Step Three
Find the roots. Use the quadratic equation. Note that the graph shows us that the equation never crosses or touches the x axis. The roots are complex.
a = 1
b = 2
c = 5
x = -1 +/- 2i
x1 = -1 + 2i
x2 = -1 - 2i And we are done.
Answer:
The correct option is;
B
Step-by-step explanation:
The given system of inequalities are;
5·x - 4·y > 4...(1)
x + y < 2...(2)
Representing both inequalities as a function of "y", gives;
For, 5·x - 4·y > 4...(1), we have;
-4·y > 4 - 5·x
y < 4/(-4) - 5·x/(-4)
∴ y < 5·x/4 - 1
For x + y < 2...(2), we have;
y < 2 - x
Therefore, y is less than the values given by the equation of the straight line equalities, and the feasible region is given by the common region under both dashed lines representing both inequalities as shown in the attached diagram created using Microsoft Excel
The correct option is therefore, B.
