Find accurate and reliable answers to your questions on IDNLearn.com. Find the solutions you need quickly and accurately with help from our knowledgeable community.
Sagot :
To find the [tex]\( y \)[/tex]-coordinate of the vertex for the quadratic function [tex]\( y = 2x^2 + 6 \)[/tex], we can follow these steps:
1. Understand the Form of the Quadratic Function:
The quadratic function is given in the form [tex]\( y = ax^2 + bx + c \)[/tex]. In this specific function, the coefficients are:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 0 \)[/tex]
- [tex]\( c = 6 \)[/tex]
2. Find the [tex]\( x \)[/tex]-coordinate of the Vertex:
For a quadratic function [tex]\( y = ax^2 + bx + c \)[/tex], the [tex]\( x \)[/tex]-coordinate of the vertex can be found using the formula:
[tex]\[ x_{\text{vertex}} = -\frac{b}{2a} \][/tex]
Substituting the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[ x_{\text{vertex}} = -\frac{0}{2 \cdot 2} = 0 \][/tex]
3. Substitute the [tex]\( x \)[/tex]-coordinate into the Original Function:
To find the [tex]\( y \)[/tex]-coordinate of the vertex, substitute [tex]\( x_{\text{vertex}} \)[/tex] back into the original quadratic equation [tex]\( y = 2x^2 + 6 \)[/tex]:
[tex]\[ y_{\text{vertex}} = 2(0)^2 + 6 = 6 \][/tex]
Therefore, the [tex]\( y \)[/tex]-coordinate of the vertex for the quadratic function [tex]\( y = 2x^2 + 6 \)[/tex] is [tex]\(\boxed{6}\)[/tex].
1. Understand the Form of the Quadratic Function:
The quadratic function is given in the form [tex]\( y = ax^2 + bx + c \)[/tex]. In this specific function, the coefficients are:
- [tex]\( a = 2 \)[/tex]
- [tex]\( b = 0 \)[/tex]
- [tex]\( c = 6 \)[/tex]
2. Find the [tex]\( x \)[/tex]-coordinate of the Vertex:
For a quadratic function [tex]\( y = ax^2 + bx + c \)[/tex], the [tex]\( x \)[/tex]-coordinate of the vertex can be found using the formula:
[tex]\[ x_{\text{vertex}} = -\frac{b}{2a} \][/tex]
Substituting the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex]:
[tex]\[ x_{\text{vertex}} = -\frac{0}{2 \cdot 2} = 0 \][/tex]
3. Substitute the [tex]\( x \)[/tex]-coordinate into the Original Function:
To find the [tex]\( y \)[/tex]-coordinate of the vertex, substitute [tex]\( x_{\text{vertex}} \)[/tex] back into the original quadratic equation [tex]\( y = 2x^2 + 6 \)[/tex]:
[tex]\[ y_{\text{vertex}} = 2(0)^2 + 6 = 6 \][/tex]
Therefore, the [tex]\( y \)[/tex]-coordinate of the vertex for the quadratic function [tex]\( y = 2x^2 + 6 \)[/tex] is [tex]\(\boxed{6}\)[/tex].
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.