Find the coordinates of the vertex of the quadratic function y=x^2+4x+

1.	Find the coordinates of the vertex of the quadratic function y=x^2+4x+6
Answer» You have a quadratic function in the FORM y=ax2+bx+c which represents, graphically, a PARABOLA.You can start by observing that the coefficient of the x2 is positive so that your parabola has an upward concavity, i.e., has a shape like a U.Then you need to determine 3 sets of coordinates that characterize your parabola:1) The Vertex: this is the lowest point of your parabola (the bottom of your U).to find its coordinates ( xvandyv ) you use the fact that:xv=−b2a and y=−Δ4a Where Δ=b2−4ac 2) Crossing point with the y axis:This point has coordinates: ( 0,c )3) Crossing point(s) with the x axis:These are obtained PUTTING y=0 and SOLVING the corresponding second DEGREE equation: ax2+bx+c=0 If the equation doesn't have solutions ( Δ<0 ) your parabola doesn't cross the x axis.If Δ=0 your vertex is also the point of crossing with the x axis.In our case we have:enter image source here

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