The vertex on a graph, specifically for a parabola (the graph of a quadratic function), is the point that represents either the highest or lowest point on the curve. It is the "turning point" where the parabola changes direction.
- If the parabola opens upward (like a U), the vertex is the lowest point on the graph.
- If the parabola opens downward (like an upside-down U), the vertex is the highest point on the graph.
The vertex is located at the point (h,k)(h,k)(h,k) when the quadratic function is written in vertex form:
f(x)=a(x−h)2+kf(x)=a(x-h)^2+kf(x)=a(x−h)2+k
Here, hhh is the x-coordinate and kkk is the y-coordinate of the vertex
. For a quadratic function in standard form y=ax2+bx+cy=ax^2+bx+cy=ax2+bx+c, the x-coordinate of the vertex can be found using the formula:
x=−b2ax=-\frac{b}{2a}x=−2ab
Once you find xxx, substitute it back into the function to find the y-coordinate y=f(x)y=f(x)y=f(x), giving the full vertex (x,y)(x,y)(x,y)
. In summary, the vertex is the point on the graph of a parabola where the curve reaches its maximum or minimum value, and it lies on the axis of symmetry of the parabola
