At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
To find the vertex of the quadratic function given by [tex]\( y = 2x^2 + 4x + 1 \)[/tex], we can use the vertex formula. The general form for a quadratic equation is [tex]\( y = ax^2 + bx + c \)[/tex].
The x-coordinate of the vertex can be found using the formula:
[tex]\[ x = -\frac{b}{2a} \][/tex]
Here, [tex]\( a = 2 \)[/tex] and [tex]\( b = 4 \)[/tex].
1. Calculate the x-coordinate of the vertex:
[tex]\[ x = -\frac{4}{2 \cdot 2} = -\frac{4}{4} = -1 \][/tex]
2. Substitute [tex]\( x = -1 \)[/tex] back into the original quadratic equation to find the y-coordinate:
[tex]\[ y = 2(-1)^2 + 4(-1) + 1 \][/tex]
[tex]\[ y = 2(1) - 4 + 1 \][/tex]
[tex]\[ y = 2 - 4 + 1 \][/tex]
[tex]\[ y = -1 \][/tex]
Thus, the coordinates of the vertex of the given quadratic function are [tex]\( (-1, -1) \)[/tex].
The correct answer is:
B. [tex]\( (-1, -1) \)[/tex]
The x-coordinate of the vertex can be found using the formula:
[tex]\[ x = -\frac{b}{2a} \][/tex]
Here, [tex]\( a = 2 \)[/tex] and [tex]\( b = 4 \)[/tex].
1. Calculate the x-coordinate of the vertex:
[tex]\[ x = -\frac{4}{2 \cdot 2} = -\frac{4}{4} = -1 \][/tex]
2. Substitute [tex]\( x = -1 \)[/tex] back into the original quadratic equation to find the y-coordinate:
[tex]\[ y = 2(-1)^2 + 4(-1) + 1 \][/tex]
[tex]\[ y = 2(1) - 4 + 1 \][/tex]
[tex]\[ y = 2 - 4 + 1 \][/tex]
[tex]\[ y = -1 \][/tex]
Thus, the coordinates of the vertex of the given quadratic function are [tex]\( (-1, -1) \)[/tex].
The correct answer is:
B. [tex]\( (-1, -1) \)[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.