What Is The Vertex Of The Graph Of The Function Below? Y = X 2 + 10 X + 24 Y = X^2 + 10x + 24 Y = X 2 + 10 X + 24 A. ( − 5 , − 1 (-5, -1 ( − 5 , − 1 ] B. ( − 5 , 0 (-5, 0 ( − 5 , 0 ] C. ( − 4 , 0 (-4, 0 ( − 4 , 0 ] D. ( − 4 , − 1 (-4, -1 ( − 4 , − 1 ]

What is the Vertex of the Graph of the Function $y = x^2 + 10x + 24$?

The vertex of a quadratic function is a crucial point that provides valuable information about the graph's behavior. In this article, we will explore the concept of the vertex and how to find it for the given function $y = x^2 + 10x + 24$.

Understanding the Vertex

The vertex of a quadratic function is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. It is also the minimum or maximum point of the graph, depending on the direction of the parabola. The vertex is represented by the coordinates $(h, k)$, where $h$ is the x-coordinate and $k$ is the y-coordinate.

Finding the Vertex

To find the vertex of the given function $y = x^2 + 10x + 24$, we can use the formula:

$$h = -\frac{b}{2a}$$

where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term.

In this case, $a = 1$ and $b = 10$. Plugging these values into the formula, we get:

$$h = -\frac{10}{2(1)} = -5$$

Now that we have the x-coordinate of the vertex, we can find the y-coordinate by plugging $h$ into the original function:

$$y = (-5)^2 + 10(-5) + 24$$

$$y = 25 - 50 + 24$$

$$y = -1$$

Therefore, the vertex of the graph of the function $y = x^2 + 10x + 24$ is $(-5, -1)$.

Comparing with the Options

Now that we have found the vertex, let's compare it with the options provided:

A. $(-5, -1)$ B. $(-5, 0)$ C. $(-4, 0)$ D. $(-4, -1)$

As we can see, option A matches our calculated vertex.

Conclusion

In this article, we explored the concept of the vertex of a quadratic function and how to find it for the given function $y = x^2 + 10x + 24$. We used the formula $h = -\frac{b}{2a}$ to find the x-coordinate of the vertex and then plugged it into the original function to find the y-coordinate. Our calculated vertex matches option A, which is $(-5, -1)$.

What is the Vertex of the Graph of the Function $y = x^2 + 10x + 24$?

The vertex of the graph of the function $y = x^2 + 10x + 24$ is $(-5, -1)$.

Why is the Vertex Important?

The vertex is an important point in the graph of a quadratic function because it provides valuable information about the graph's behavior. It is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. The vertex is also the minimum or maximum point of the graph, depending on the direction of the parabola.

How to Find the Vertex

To find the vertex of a quadratic function, you can use the formula $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term. Once you have the x-coordinate of the vertex, you can plug it into the original function to find the y-coordinate.

What is the Formula for the Vertex?

The formula for the vertex is $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term.

What is the X-Coordinate of the Vertex?

The x-coordinate of the vertex is $h = -\frac{b}{2a}$.

What is the Y-Coordinate of the Vertex?

The y-coordinate of the vertex is found by plugging the x-coordinate into the original function.

What is the Vertex of the Graph of the Function $y = x^2 + 10x + 24$?

The vertex of the graph of the function $y = x^2 + 10x + 24$ is $(-5, -1)$.

Why is the Vertex Important in Real-World Applications?

The vertex is an important point in the graph of a quadratic function because it provides valuable information about the graph's behavior. It is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. The vertex is also the minimum or maximum point of the graph, depending on the direction of the parabola.

How to Use the Vertex in Real-World Applications

To use the vertex in real-world applications, you can use the formula $h = -\frac{b}{2a}$ to find the x-coordinate of the vertex and then plug it into the original function to find the y-coordinate. This can be useful in a variety of fields, including physics, engineering, and economics.

What is the Formula for the Vertex in Terms of the Coefficients?

The formula for the vertex in terms of the coefficients is $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term.

What is the X-Coordinate of the Vertex in Terms of the Coefficients?

The x-coordinate of the vertex in terms of the coefficients is $h = -\frac{b}{2a}$.

What is the Y-Coordinate of the Vertex in Terms of the Coefficients?

The y-coordinate of the vertex in terms of the coefficients is found by plugging the x-coordinate into the original function.

What is the Vertex of the Graph of the Function $y = x^2 + 10x + 24$?

The vertex of the graph of the function $y = x^2 + 10x + 24$ is $(-5, -1)$.

Why is the Vertex Important in Algebra?

The vertex is an important point in the graph of a quadratic function because it provides valuable information about the graph's behavior. It is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. The vertex is also the minimum or maximum point of the graph, depending on the direction of the parabola.

How to Use the Vertex in Algebra

To use the vertex in algebra, you can use the formula $h = -\frac{b}{2a}$ to find the x-coordinate of the vertex and then plug it into the original function to find the y-coordinate. This can be useful in a variety of algebraic applications, including solving quadratic equations and graphing quadratic functions.

What is the Formula for the Vertex in Algebra?

The formula for the vertex in algebra is $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term.

What is the X-Coordinate of the Vertex in Algebra?

The x-coordinate of the vertex in algebra is $h = -\frac{b}{2a}$.

What is the Y-Coordinate of the Vertex in Algebra?

The y-coordinate of the vertex in algebra is found by plugging the x-coordinate into the original function.

What is the Vertex of the Graph of the Function $y = x^2 + 10x + 24$?

The vertex of the graph of the function $y = x^2 + 10x + 24$ is $(-5, -1)$.

Why is the Vertex Important in Calculus?

The vertex is an important point in the graph of a quadratic function because it provides valuable information about the graph's behavior. It is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. The vertex is also the minimum or maximum point of the graph, depending on the direction of the parabola.

How to Use the Vertex in Calculus

To use the vertex in calculus, you can use the formula $h = -\frac{b}{2a}$ to find the x-coordinate of the vertex and then plug it into the original function to find the y-coordinate. This can be useful in a variety of calculus applications, including finding the derivative and integral of quadratic functions.

What is the Formula for the Vertex in Calculus?

The formula for the vertex in calculus is $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term.

What is the X-Coordinate of the Vertex in Calculus?

The x-coordinate of the vertex in calculus is $h = -\frac{b}{2a}$.

What is the Y-Coordinate of the Vertex in Calculus?

The y-coordinate of the vertex in calculus is found by plugging the x-coordinate into the original function.

What is the Vertex of the Graph of the Function $y = x^2 + 10x + 24$?

The vertex of the graph of the function $y = x^2 + 10x + 24$ is $(-5, -1)$.

Why is the Vertex Important in Real-World Applications?

The vertex is an important point in the graph of a quadratic function because it provides valuable information about the graph's behavior. It is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. The vertex is
Q&A: What is the Vertex of the Graph of the Function $y = x^2 + 10x + 24$?

Q: What is the vertex of a quadratic function?

A: The vertex of a quadratic function is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. It is also the minimum or maximum point of the graph, depending on the direction of the parabola.

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 $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term. Once you have the x-coordinate of the vertex, you can plug it into the original function to find the y-coordinate.

Q: What is the formula for the vertex in terms of the coefficients?

A: The formula for the vertex in terms of the coefficients is $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term.

Q: What is the x-coordinate of the vertex in terms of the coefficients?

A: The x-coordinate of the vertex in terms of the coefficients is $h = -\frac{b}{2a}$.

Q: What is the y-coordinate of the vertex in terms of the coefficients?

A: The y-coordinate of the vertex in terms of the coefficients is found by plugging the x-coordinate into the original function.

Q: How do I use the vertex in real-world applications?

A: To use the vertex in real-world applications, you can use the formula $h = -\frac{b}{2a}$ to find the x-coordinate of the vertex and then plug it into the original function to find the y-coordinate. This can be useful in a variety of fields, including physics, engineering, and economics.

Q: What is the vertex of the graph of the function $y = x^2 + 10x + 24$?

A: The vertex of the graph of the function $y = x^2 + 10x + 24$ is $(-5, -1)$.

Q: Why is the vertex important in algebra?

A: The vertex is an important point in the graph of a quadratic function because it provides valuable information about the graph's behavior. It is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. The vertex is also the minimum or maximum point of the graph, depending on the direction of the parabola.

Q: How do I use the vertex in algebra?

A: To use the vertex in algebra, you can use the formula $h = -\frac{b}{2a}$ to find the x-coordinate of the vertex and then plug it into the original function to find the y-coordinate. This can be useful in a variety of algebraic applications, including solving quadratic equations and graphing quadratic functions.

Q: What is the formula for the vertex in algebra?

A: The formula for the vertex in algebra is $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term.

Q: What is the x-coordinate of the vertex in algebra?

A: The x-coordinate of the vertex in algebra is $h = -\frac{b}{2a}$.

Q: What is the y-coordinate of the vertex in algebra?

A: The y-coordinate of the vertex in algebra is found by plugging the x-coordinate into the original function.

Q: Why is the vertex important in calculus?

A: The vertex is an important point in the graph of a quadratic function because it provides valuable information about the graph's behavior. It is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. The vertex is also the minimum or maximum point of the graph, depending on the direction of the parabola.

Q: How do I use the vertex in calculus?

A: To use the vertex in calculus, you can use the formula $h = -\frac{b}{2a}$ to find the x-coordinate of the vertex and then plug it into the original function to find the y-coordinate. This can be useful in a variety of calculus applications, including finding the derivative and integral of quadratic functions.

Q: What is the formula for the vertex in calculus?

A: The formula for the vertex in calculus is $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term.

Q: What is the x-coordinate of the vertex in calculus?

A: The x-coordinate of the vertex in calculus is $h = -\frac{b}{2a}$.

Q: What is the y-coordinate of the vertex in calculus?

A: The y-coordinate of the vertex in calculus is found by plugging the x-coordinate into the original function.

Q: What is the vertex of the graph of the function $y = x^2 + 10x + 24$?

A: The vertex of the graph of the function $y = x^2 + 10x + 24$ is $(-5, -1)$.

Q: Why is the vertex important in real-world applications?

A: The vertex is an important point in the graph of a quadratic function because it provides valuable information about the graph's behavior. It is the point where the graph changes direction, from either increasing to decreasing or decreasing to increasing. The vertex is also the minimum or maximum point of the graph, depending on the direction of the parabola.

Q: How do I use the vertex in real-world applications?

A: To use the vertex in real-world applications, you can use the formula $h = -\frac{b}{2a}$ to find the x-coordinate of the vertex and then plug it into the original function to find the y-coordinate. This can be useful in a variety of fields, including physics, engineering, and economics.

Q: What is the formula for the vertex in real-world applications?

A: The formula for the vertex in real-world applications is $h = -\frac{b}{2a}$, where $a$ is the coefficient of the squared term and $b$ is the coefficient of the linear term.

Q: What is the x-coordinate of the vertex in real-world applications?

A: The x-coordinate of the vertex in real-world applications is $h = -\frac{b}{2a}$.

Q: What is the y-coordinate of the vertex in real-world applications?

A: The y-coordinate of the vertex in real-world applications is found by plugging the x-coordinate into the original function.

Q: What is the vertex of the graph of the function $y = x^2 + 10x + 24$?

A: The vertex of the graph of the function $y = x^2 + 10x + 24$ is $(-5, -1)$.