Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To find the [tex]\( y \)[/tex]-value of the vertex of a quadratic function given by [tex]\( y = ax^2 + bx + c \)[/tex], follow these steps:
1. Identify the [tex]\( x \)[/tex]-value of the vertex:
The [tex]\( x \)[/tex]-value of the vertex of a quadratic function can be found using the formula:
[tex]\[ x = -\frac{b}{2a} \][/tex]
For typical values [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = 1 \)[/tex], this would give:
[tex]\[ x = -\frac{1}{2 \cdot 1} = -0.5 \][/tex]
2. Substitute the [tex]\( x \)[/tex]-value into the quadratic equation:
Once you have the [tex]\( x \)[/tex]-value of the vertex, substitute it back into the original quadratic equation to find the corresponding [tex]\( y \)[/tex]-value.
[tex]\[ y = a \left(-0.5 \right)^2 + b \left(-0.5 \right) + c \][/tex]
Using the values [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = 1 \)[/tex]:
[tex]\[ y = 1 \left(-0.5 \right)^2 + 1 \left(-0.5 \right) + 1 \][/tex]
Calculate each term individually:
[tex]\[ \left(-0.5 \right)^2 = 0.25 \][/tex]
[tex]\[ 1 \cdot 0.25 = 0.25 \][/tex]
[tex]\[ 1 \cdot -0.5 = -0.5 \][/tex]
[tex]\[ y = 0.25 - 0.5 + 1 \][/tex]
[tex]\[ y = 0.75 \][/tex]
3. Combine the results:
So, the [tex]\( y \)[/tex]-value of the vertex when [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = 1 \)[/tex] is:
[tex]\[ y = 0.75 \][/tex]
Thus, the coordinates of the vertex of the quadratic function given by [tex]\( y = ax^2 + bx + c \)[/tex] with values [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = 1 \)[/tex] are [tex]\( (-0.5, 0.75) \)[/tex].
1. Identify the [tex]\( x \)[/tex]-value of the vertex:
The [tex]\( x \)[/tex]-value of the vertex of a quadratic function can be found using the formula:
[tex]\[ x = -\frac{b}{2a} \][/tex]
For typical values [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = 1 \)[/tex], this would give:
[tex]\[ x = -\frac{1}{2 \cdot 1} = -0.5 \][/tex]
2. Substitute the [tex]\( x \)[/tex]-value into the quadratic equation:
Once you have the [tex]\( x \)[/tex]-value of the vertex, substitute it back into the original quadratic equation to find the corresponding [tex]\( y \)[/tex]-value.
[tex]\[ y = a \left(-0.5 \right)^2 + b \left(-0.5 \right) + c \][/tex]
Using the values [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = 1 \)[/tex]:
[tex]\[ y = 1 \left(-0.5 \right)^2 + 1 \left(-0.5 \right) + 1 \][/tex]
Calculate each term individually:
[tex]\[ \left(-0.5 \right)^2 = 0.25 \][/tex]
[tex]\[ 1 \cdot 0.25 = 0.25 \][/tex]
[tex]\[ 1 \cdot -0.5 = -0.5 \][/tex]
[tex]\[ y = 0.25 - 0.5 + 1 \][/tex]
[tex]\[ y = 0.75 \][/tex]
3. Combine the results:
So, the [tex]\( y \)[/tex]-value of the vertex when [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = 1 \)[/tex] is:
[tex]\[ y = 0.75 \][/tex]
Thus, the coordinates of the vertex of the quadratic function given by [tex]\( y = ax^2 + bx + c \)[/tex] with values [tex]\( a = 1 \)[/tex], [tex]\( b = 1 \)[/tex], and [tex]\( c = 1 \)[/tex] are [tex]\( (-0.5, 0.75) \)[/tex].
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.