The vertex of a parabola is the point where the parabola crosses its axis of symmetry. If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “U”-shape. If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “U”-shape.The standard equation of a parabola isy = ax2 + bx + c.But the equation for a parabola can also be written in "vertex form":y = a(x – h)2 + kIn this equation, the vertex of the parabola is the point (h, k).You can see how this relates to the standard equation by multiplying it out:y = a(x – h)(x – h) + ky = ax2 – 2ahx + ah2 + kThe coefficient of x here is –2ah. This means that in the standard form, y = ax2 + bx + c, the expressiongives the x-coordinate of the vertex.Example:Find the vertex of the parabola.y = 3x2 + 12x – 12Here, a = 3 and b = 12. So, the x-coordinate of the vertex is:Substituting in the original equation to get the y-coordinate, we get:y = 3(–2)2 + 12(–2) – 12= –24So, the vertex of the parabola is at (–2, –24).
