Goutamaida9y2

 If you mean G(x) = x² 4x (I'll use a 'y' instead of a 'G(x)') Complete the square y 4 = x² 4x 4 Factor y 4 = (x 2)² Any equation in the form y k = (x h)² is a parabola with its vertex at (h, k); altavistardaltavistard Answer y = (x 2)^2 7 Stepbystep explanation The vertex form of the equation of a parabola (such as we have here) is y = a(xh)^2 k, where (h,k) is the vertex It's safe to assume that the coefficient "a" in y=x^24x3 is 1 The best thing to do now is to complete the squareDivide 1, the coefficient of the x term, by 2 to get \frac {1} {2} Then add the square of \frac {1} {2} to both sides of the equation This step makes the left hand side of the equation a perfect square x^ {2}x\frac {1} {4}=\frac {y11} {4} Plot A Graph For The Equation Y X 2 4x 1 Y=x^2-4x 1 vertex

5 2 Quadratic Functions Mathematics Libretexts  Replace h with the y coordinate of the vertex and k with the x coordinate In the example shown in the picture, the vertex is the origin, (0, 0) so there will be no h and k , simplifying the equation to x = a y 2 {\displaystyle x=ay^{2}}For any given parabola whose equation has the form \(y=a(xh)^2k\text{,}\) the vertical line \(x=h\) is called the axis of symmetry for the parabolaPrintable pages make math easy Are you ready to be a mathmagician? Parabola equation y-k=a(x-h)^2