Question
Identify the vertex and axis of symmetry of the parabola. (1 point) axis of symmetry: x= vertex: ()
Answers
GPT-4o mini
To identify the vertex and axis of symmetry of a parabola, we typically start with the standard form of a quadratic equation, \( y = ax^2 + bx + c \).
1. **Axis of symmetry**: The formula for the axis of symmetry of a parabola given by the equation \( y = ax^2 + bx + c \) is:
\[
x = -\frac{b}{2a}
\]
2. **Vertex**: The vertex can be found using the axis of symmetry. Once we calculate \( x \) from the axis of symmetry, we can substitute it back into the equation to find the \( y \)-coordinate of the vertex:
\[
y = a\left(-\frac{b}{2a}\right)^2 + b\left(-\frac{b}{2a}\right) + c
\]
This gives the coordinates of the vertex as:
\[
\left(-\frac{b}{2a}, y\right)
\]
If you provide the quadratic equation, I can help you calculate the vertex and the axis of symmetry specifically for that parabola.
1. **Axis of symmetry**: The formula for the axis of symmetry of a parabola given by the equation \( y = ax^2 + bx + c \) is:
\[
x = -\frac{b}{2a}
\]
2. **Vertex**: The vertex can be found using the axis of symmetry. Once we calculate \( x \) from the axis of symmetry, we can substitute it back into the equation to find the \( y \)-coordinate of the vertex:
\[
y = a\left(-\frac{b}{2a}\right)^2 + b\left(-\frac{b}{2a}\right) + c
\]
This gives the coordinates of the vertex as:
\[
\left(-\frac{b}{2a}, y\right)
\]
If you provide the quadratic equation, I can help you calculate the vertex and the axis of symmetry specifically for that parabola.