To identify the vertex of a quadratic function represented by a curved line (parabola) that passes through specific \( x \) values (like \( x = -12 \) and \( x = -10 \)), you can follow these steps:
-
Determine the Midpoint: The vertex of a parabola in standard form \( y = ax^2 + bx + c \) lies on the axis of symmetry, which is halfway between the two \( x \) values where the parabola intersects the axis (in this case, \( x = -12 \) and \( x = -10 \)).
\[ \text{Midpoint} = \frac{x_1 + x_2}{2} = \frac{-12 + (-10)}{2} = \frac{-22}{2} = -11 \]
-
Find the \( y \)-Value of the Vertex: If you have the equation of the parabola, you can substitute \( x = -11 \) into the equation to find the corresponding \( y \)-value (the \( y \)-coordinate of the vertex).
If the equation of the curve is not provided, you cannot determine the exact value of \( y \) without additional information about the specific function.
- Vertex Form: If the parabola is in vertex form \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex, then from step 1, \( h = -11 \).
In summary, the \( x \)-coordinate of the vertex is \( -11 \), and you would need the exact function to find the \( y \)-coordinate. If you have more details about the function, feel free to provide that for further assistance!