The vertex is either the highest or lowest point on the graph depending on whether it opens up or down. A parabola for a quadratic function can open up or down, but not left or right. Use symmetry to plot two more points, such as (3, 0) and (4, 6).ĭraw a parabola through the plotted points. The basics The graph of a quadratic function is a parabola. Plot two points on one side of the axis of symmetry, such as (1, 0) and (0, 6). The x-coordinate at the vertex is 2 and axis of symmetry is x = 2. The axis of symmetry is halfway between (p, 0) and (q, 0).įor all the three forms, the graph opens up if a > 0 and opens down if a 0, the parabola opens up.įind and plot the vertex. Intercept form of a quadratic function is , origin, quadrants Points in the Coordinate plane Midpoint of a line segment. Graphing a quadratic function Transformations of the graph of the quadratic function. Two other useful forms for quadratic functions are given below. Quadratic Equations and Quadratic Function.
Now plug in the points given: (-1,3) a 3 Plug a back in. Therefore, you plug in (0,0) for h and k. The axis of symmetry is the vertical line x = -b/2a. Answer (1 of 7): The vertex form of a quadratic equation is where (h,k) is the vertex and a is a constant.The x-coordinate of the vertex is -b/2a.The parabola opens up if a > 0 and opens down if a 1.The graph of y = ax 2 + bx + c is a parabola with these characteristics : The graph of the more general function y = ax 2 + bx + c is described below. In general, the axis of symmetry for the graph of a quadratic function is the vertical line through the vertex. The graphs of y = x 2 and y = -x 2 are symmetric about the y-axis, called the axis of symmetry.