At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Ask your questions and receive precise answers from experienced professionals across different disciplines. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To identify the vertex of the quadratic equation [tex]\( y = x^2 + 4x + 3 \)[/tex], let's follow these steps:
1. Understand the standard form of a quadratic equation:
A quadratic equation is typically written in the form [tex]\( y = ax^2 + bx + c \)[/tex], where:
- [tex]\( a \)[/tex] is the coefficient of [tex]\( x^2 \)[/tex]
- [tex]\( b \)[/tex] is the coefficient of [tex]\( x \)[/tex]
- [tex]\( c \)[/tex] is the constant term
For the given equation [tex]\( y = x^2 + 4x + 3 \)[/tex]:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = 4 \)[/tex]
- [tex]\( c = 3 \)[/tex]
2. Identify the x-coordinate of the vertex:
The x-coordinate of the vertex can be found using the formula [tex]\( x = -\frac{b}{2a} \)[/tex].
Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the formula:
[tex]\[ x = -\frac{4}{2 \cdot 1} = -\frac{4}{2} = -2 \][/tex]
3. Identify the y-coordinate of the vertex:
Once we have the x-coordinate, we substitute [tex]\( x = -2 \)[/tex] back into the original equation to find the y-coordinate.
Substitute [tex]\( x = -2 \)[/tex] into [tex]\( y = x^2 + 4x + 3 \)[/tex]:
[tex]\[ y = (-2)^2 + 4(-2) + 3 \][/tex]
Calculate each term:
[tex]\[ y = 4 - 8 + 3 = -1 \][/tex]
4. Determine the vertex:
With the x-coordinate as [tex]\(-2\)[/tex] and the y-coordinate as [tex]\(-1\)[/tex], the vertex of the quadratic equation [tex]\( y = x^2 + 4x + 3 \)[/tex] is:
[tex]\[ (-2, -1) \][/tex]
5. Identify the correct option:
Based on the options provided:
- [tex]\( \boxed{(-2, -1)} \)[/tex] is the correct answer.
So, the vertex of the equation [tex]\( y = x^2 + 4x + 3 \)[/tex] is [tex]\( (-2, -1) \)[/tex]. Therefore, the correct option is B.
1. Understand the standard form of a quadratic equation:
A quadratic equation is typically written in the form [tex]\( y = ax^2 + bx + c \)[/tex], where:
- [tex]\( a \)[/tex] is the coefficient of [tex]\( x^2 \)[/tex]
- [tex]\( b \)[/tex] is the coefficient of [tex]\( x \)[/tex]
- [tex]\( c \)[/tex] is the constant term
For the given equation [tex]\( y = x^2 + 4x + 3 \)[/tex]:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = 4 \)[/tex]
- [tex]\( c = 3 \)[/tex]
2. Identify the x-coordinate of the vertex:
The x-coordinate of the vertex can be found using the formula [tex]\( x = -\frac{b}{2a} \)[/tex].
Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the formula:
[tex]\[ x = -\frac{4}{2 \cdot 1} = -\frac{4}{2} = -2 \][/tex]
3. Identify the y-coordinate of the vertex:
Once we have the x-coordinate, we substitute [tex]\( x = -2 \)[/tex] back into the original equation to find the y-coordinate.
Substitute [tex]\( x = -2 \)[/tex] into [tex]\( y = x^2 + 4x + 3 \)[/tex]:
[tex]\[ y = (-2)^2 + 4(-2) + 3 \][/tex]
Calculate each term:
[tex]\[ y = 4 - 8 + 3 = -1 \][/tex]
4. Determine the vertex:
With the x-coordinate as [tex]\(-2\)[/tex] and the y-coordinate as [tex]\(-1\)[/tex], the vertex of the quadratic equation [tex]\( y = x^2 + 4x + 3 \)[/tex] is:
[tex]\[ (-2, -1) \][/tex]
5. Identify the correct option:
Based on the options provided:
- [tex]\( \boxed{(-2, -1)} \)[/tex] is the correct answer.
So, the vertex of the equation [tex]\( y = x^2 + 4x + 3 \)[/tex] is [tex]\( (-2, -1) \)[/tex]. Therefore, the correct option is B.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.