Identify All The Points That Are On The Following Quadratic Function: $y = X^2 - 3x$A. $(-3, 15$\]B. $(0, 0$\]C. $(0, 3$\]D. $(2, -2$\]E. $(-1, 4$\]

Introduction

Quadratic functions are a fundamental concept in mathematics, and understanding how to identify points on these functions is crucial for solving various mathematical problems. In this article, we will explore the quadratic function $y = x^2 - 3x$ and identify the points that lie on this function.

Understanding Quadratic Functions

A quadratic function is a polynomial function of degree two, which means the highest power of the variable (in this case, $x$) is two. The general form of a quadratic function is $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants. In our case, the quadratic function is $y = x^2 - 3x$.

Identifying Points on the Quadratic Function

To identify the points on the quadratic function $y = x^2 - 3x$, we need to substitute the given values of $x$ into the function and solve for $y$. Let's examine each option:

A. $(-3, 15)$

To verify if the point $(-3, 15)$ lies on the quadratic function, we substitute $x = -3$ into the function:

$$y = (-3)^2 - 3(-3)$$

$$y = 9 + 9$$

$$y = 18$$

Since $y = 18$ is not equal to $15$, the point $(-3, 15)$ does not lie on the quadratic function.

B. $(0, 0)$

To verify if the point $(0, 0)$ lies on the quadratic function, we substitute $x = 0$ into the function:

$$y = (0)^2 - 3(0)$$

$$y = 0$$

Since $y = 0$ is equal to $0$, the point $(0, 0)$ lies on the quadratic function.

C. $(0, 3)$

To verify if the point $(0, 3)$ lies on the quadratic function, we substitute $x = 0$ into the function:

$$y = (0)^2 - 3(0)$$

$$y = 0$$

Since $y = 0$ is not equal to $3$, the point $(0, 3)$ does not lie on the quadratic function.

D. $(2, -2)$

To verify if the point $(2, -2)$ lies on the quadratic function, we substitute $x = 2$ into the function:

$$y = (2)^2 - 3(2)$$

$$y = 4 - 6$$

$$y = -2$$

Since $y = -2$ is equal to $-2$, the point $(2, -2)$ lies on the quadratic function.

E. $(-1, 4)$

To verify if the point $(-1, 4)$ lies on the quadratic function, we substitute $x = -1$ into the function:

$$y = (-1)^2 - 3(-1)$$

$$y = 1 + 3$$

$$y = 4$$

Since $y = 4$ is equal to $4$, the point $(-1, 4)$ lies on the quadratic function.

Conclusion

In this article, we identified the points that lie on the quadratic function $y = x^2 - 3x$. We found that the points $(0, 0)$, $(2, -2)$, and $(-1, 4)$ lie on the quadratic function, while the points $(-3, 15)$ and $(0, 3)$ do not. Understanding how to identify points on quadratic functions is essential for solving various mathematical problems, and we hope this article has provided a clear and concise guide on how to do so.

Key Takeaways

• A quadratic function is a polynomial function of degree two.
• The general form of a quadratic function is $y = ax^2 + bx + c$.
• To identify points on a quadratic function, substitute the given values of $x$ into the function and solve for $y$.
• The points $(0, 0)$, $(2, -2)$, and $(-1, 4)$ lie on the quadratic function $y = x^2 - 3x$.
• The points $(-3, 15)$ and $(0, 3)$ do not lie on the quadratic function $y = x^2 - 3x$.

Further Reading

For more information on quadratic functions and how to identify points on them, we recommend checking out the following resources:

• Khan Academy: Quadratic Functions
• Math Is Fun: Quadratic Functions
• Wolfram MathWorld: Quadratic Function
  Quadratic Function Q&A: Identifying Points and More =====================================================

Introduction

In our previous article, we explored the quadratic function $y = x^2 - 3x$ and identified the points that lie on this function. In this article, we will answer some frequently asked questions about quadratic functions and provide additional information to help you better understand these functions.

Q&A

Q: What is a quadratic function?

A: A quadratic function is a polynomial function of degree two, which means the highest power of the variable (in this case, $x$) is two. The general form of a quadratic function is $y = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants.

Q: How do I identify points on a quadratic function?

A: To identify points on a quadratic function, substitute the given values of $x$ into the function and solve for $y$. For example, if we want to find the point on the quadratic function $y = x^2 - 3x$ when $x = 2$, we would substitute $x = 2$ into the function and solve for $y$.

Q: What is the vertex of a quadratic function?

A: The vertex of a quadratic function is the point on the function where the function changes direction. The vertex can be found using the formula $x = -\frac{b}{2a}$, where $a$ and $b$ are the coefficients of the quadratic function.

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

A: To find the vertex of a quadratic function, we can use the formula $x = -\frac{b}{2a}$. For example, if we have the quadratic function $y = x^2 - 3x$, we can find the vertex by substituting $a = 1$ and $b = -3$ into the formula.

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

A: The axis of symmetry of a quadratic function is a vertical line that passes through the vertex of the function. The equation of the axis of symmetry is $x = -\frac{b}{2a}$.

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

A: To find the axis of symmetry of a quadratic function, we can use the formula $x = -\frac{b}{2a}$. For example, if we have the quadratic function $y = x^2 - 3x$, we can find the axis of symmetry by substituting $a = 1$ and $b = -3$ into the formula.

Q: What is the x-intercept of a quadratic function?

A: The x-intercept of a quadratic function is the point on the function where the function crosses the x-axis. The x-intercept can be found by setting $y = 0$ and solving for $x$.

Q: How do I find the x-intercept of a quadratic function?

A: To find the x-intercept of a quadratic function, we can set $y = 0$ and solve for $x$. For example, if we have the quadratic function $y = x^2 - 3x$, we can find the x-intercept by setting $y = 0$ and solving for $x$.

Q: What is the y-intercept of a quadratic function?

A: The y-intercept of a quadratic function is the point on the function where the function crosses the y-axis. The y-intercept can be found by setting $x = 0$ and solving for $y$.

Q: How do I find the y-intercept of a quadratic function?

A: To find the y-intercept of a quadratic function, we can set $x = 0$ and solve for $y$. For example, if we have the quadratic function $y = x^2 - 3x$, we can find the y-intercept by setting $x = 0$ and solving for $y$.

Conclusion

In this article, we answered some frequently asked questions about quadratic functions and provided additional information to help you better understand these functions. We hope this article has been helpful in clarifying any confusion you may have had about quadratic functions.

Key Takeaways

• A quadratic function is a polynomial function of degree two.
• The general form of a quadratic function is $y = ax^2 + bx + c$.
• To identify points on a quadratic function, substitute the given values of $x$ into the function and solve for $y$.
• The vertex of a quadratic function is the point on the function where the function changes direction.
• The axis of symmetry of a quadratic function is a vertical line that passes through the vertex of the function.
• The x-intercept of a quadratic function is the point on the function where the function crosses the x-axis.
• The y-intercept of a quadratic function is the point on the function where the function crosses the y-axis.

Further Reading

For more information on quadratic functions and how to identify points on them, we recommend checking out the following resources:

• Khan Academy: Quadratic Functions
• Math Is Fun: Quadratic Functions
• Wolfram MathWorld: Quadratic Function