A Parabola is type of conic section whose graph has u - shape that is vertex Point lies at the center (symmetrical Geometry). It also intersects at one point on each of 'x' and y- axes. In standard form equation of parabola can be given as:
Y - K = A (X - H) 2 . Where, (K, H) represents the coordinates of vertex of parabola. Let us understand how to graph a parabola in standard form. For this consider an example of parabola whose equation is given as: y - 6 = - 1 / 6 (x + 6)2, equation 1.
First step is to find vertex of parabola. As we know that vertex is exact center, using formula for parabola, Y - K = A (X - H)2, x - coordinate (horizontal) of the vertex is "H = - 6" and y - coordinate (vertical) of the vertex "K = 6."
Next we need to find Intersection point of parabola with y – axis (y – intercept) by solving equation 1 for "y." Substitute values of x: At x = 0, y = 0.
Similarly solving equation for 'x' by substituting y = 0 in equation 1 we get: x = 0 or -12. We get two values for 'x' because root sign which means both positive and negative (+/-) results or solutions. As parabola in general goes to infinity, this can be shown by leaving two ends of parabola where graph ends.
Graph your parabola on horizontal and vertical axes. First plot 'x' and y- intercept points on graph. Then connect these points making a u- shaped line representing your parabolic equation. Let two ends of u- shape approach to infinity.