A) Complete The Table Of Values For Y = X 2 + 2 X − 2 Y = X^2 + 2x - 2 Y = X 2 + 2 X − 2 .${ \begin{array}{|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 \ \hline y & 6 & 1 & -2 & -3 & -2 & 1 & 6 \ \hline \end{array} }$b) I) Which Of The Three Curves

Introduction

In this article, we will be completing the table of values for the quadratic function $y = x^2 + 2x - 2$. We will also be discussing the properties of the resulting curve and comparing it with other quadratic functions.

The Quadratic Function

The quadratic function is given by the equation $y = x^2 + 2x - 2$. This function can be graphed on a coordinate plane, with the x-axis representing the input values and the y-axis representing the output values.

Completing the Table of Values

To complete the table of values, we need to find the corresponding y-values for the given x-values. We can do this by plugging in the x-values into the equation $y = x^2 + 2x - 2$.

x	y
-4	6
-3	1
-2	-2
-1	-3
0	-2
1	1
2	6

Calculating the Missing Values

To calculate the missing values, we can use the equation $y = x^2 + 2x - 2$. Let's calculate the y-values for x = 3, 4, and 5.

For x = 3: $y = (3)^2 + 2(3) - 2$ $y = 9 + 6 - 2$ $y = 13$

For x = 4: $y = (4)^2 + 2(4) - 2$ $y = 16 + 8 - 2$ $y = 22$

For x = 5: $y = (5)^2 + 2(5) - 2$ $y = 25 + 10 - 2$ $y = 33$

The Completed Table of Values

Here is the completed table of values:

x	y
-4	6
-3	1
-2	-2
-1	-3
0	-2
1	1
2	6
3	13
4	22
5	33

Graphing the Quadratic Function

The quadratic function $y = x^2 + 2x - 2$ can be graphed on a coordinate plane. The graph will be a parabola that opens upwards.

Comparing with Other Quadratic Functions

Let's compare the quadratic function $y = x^2 + 2x - 2$ with other quadratic functions. We can do this by graphing the functions on the same coordinate plane.

Discussion

The quadratic function $y = x^2 + 2x - 2$ is a parabola that opens upwards. The graph of the function is symmetric about the axis of symmetry, which is the vertical line x = -1.

Conclusion

In this article, we completed the table of values for the quadratic function $y = x^2 + 2x - 2$. We also graphed the function and compared it with other quadratic functions. The graph of the function is a parabola that opens upwards, and the axis of symmetry is the vertical line x = -1.

References

• [1] "Quadratic Functions" by Math Open Reference
• [2] "Graphing Quadratic Functions" by Khan Academy

Additional Resources

• [1] "Quadratic Functions" by Wolfram MathWorld
• [2] "Graphing Quadratic Functions" by Purplemath

Table of Values for Other Quadratic Functions

Here are the tables of values for other quadratic functions:

x	y = x^2 - 4x + 3
-4	27
-3	12
-2	-1
-1	-6
0	-3
1	-4
2	-1
x	y = x^2 + 6x + 8
---	---
-4	0
-3	9
-2	20
-1	33
0	8
1	13
2	20
x	y = x^2 - 2x - 3
---	---
-4	19
-3	6
-2	-1
-1	-6
0	-3
1	-4
2	-1

Conclusion

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Introduction

In this article, we will be answering some frequently asked questions about quadratic functions. Quadratic functions are a type of polynomial function that can be written in the form $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

Q&A

Q: What is a quadratic function?

A: A quadratic function is a type of polynomial function that can be written in the form $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

Q: What is the general form of a quadratic function?

A: The general form of a quadratic function is $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

Q: What is the axis of symmetry of a quadratic function?

A: The axis of symmetry of a quadratic function is the vertical line that passes through the vertex of the parabola. It can be found using the formula $x = -\frac{b}{2a}$.

Q: How do I find the vertex of a quadratic function?

A: To find the vertex of a quadratic function, you can use the formula $x = -\frac{b}{2a}$. This will give you the x-coordinate of the vertex. To find the y-coordinate, plug the x-coordinate back into the equation of the quadratic function.

Q: What is the difference between a quadratic function and a linear function?

A: A quadratic function is a polynomial function of degree 2, while a linear function is a polynomial function of degree 1. Quadratic functions have a parabolic shape, while linear functions have a straight line shape.

Q: Can a quadratic function have a negative leading coefficient?

A: Yes, a quadratic function can have a negative leading coefficient. For example, the quadratic function $y = -x^2 + 2x - 1$ has a negative leading coefficient.

Q: How do I graph a quadratic function?

A: To graph a quadratic function, you can use the following steps:

1. Find the vertex of the parabola using the formula $x = -\frac{b}{2a}$.
2. Find the y-coordinate of the vertex by plugging the x-coordinate back into the equation of the quadratic function.
3. Plot the vertex on the coordinate plane.
4. Use the axis of symmetry to plot the other points on the parabola.
5. Draw a smooth curve through the points to complete the graph.

Q: Can a quadratic function have a complex root?

A: Yes, a quadratic function can have a complex root. For example, the quadratic function $y = x^2 + 1$ has a complex root.

Q: How do I find the roots of a quadratic function?

A: To find the roots of a quadratic function, you can use the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Q: Can a quadratic function have a rational root?

A: Yes, a quadratic function can have a rational root. For example, the quadratic function $y = x^2 - 4x + 4$ has a rational root.

Q: How do I determine if a quadratic function is increasing or decreasing?

A: To determine if a quadratic function is increasing or decreasing, you can use the following steps:

1. Find the derivative of the quadratic function.
2. Set the derivative equal to zero and solve for x.
3. If the derivative is positive, the function is increasing. If the derivative is negative, the function is decreasing.

Q: Can a quadratic function have a maximum or minimum value?

A: Yes, a quadratic function can have a maximum or minimum value. For example, the quadratic function $y = x^2 - 4x + 4$ has a minimum value.

Q: How do I find the maximum or minimum value of a quadratic function?

A: To find the maximum or minimum value of a quadratic function, you can use the following steps:

1. Find the vertex of the parabola using the formula $x = -\frac{b}{2a}$.
2. Find the y-coordinate of the vertex by plugging the x-coordinate back into the equation of the quadratic function.
3. The y-coordinate of the vertex is the maximum or minimum value of the function.

Conclusion

In this article, we answered some frequently asked questions about quadratic functions. Quadratic functions are a type of polynomial function that can be written in the form $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants. We discussed the general form of a quadratic function, the axis of symmetry, and how to find the vertex of a quadratic function. We also discussed how to graph a quadratic function, find the roots of a quadratic function, and determine if a quadratic function is increasing or decreasing.