![]() ![]() ![]() The general equation of a quadratic function is f(x) = ax 2 + bx + c. Graphing Quadratic Functions in Standard Form The graph of quadratic functions can also be obtained using the graphing quadratic functions calculator. The following figure shows an example shift: The final vertex of the parabola will be at (-b/2a, -D/4a). The direction of the shift will be decided by the sign of D/4a. Step 3: a(x + b/2a) 2 to a(x + b/2a) 2 - D/4a: This transformation is a vertical shift of magnitude |D/4a| units.The new vertex of the parabola will be at (-b/2a,0). The direction of the shift will be decided by the sign of b/2a. Step 2: ax 2 to a(x + b/2a) 2: This is a horizontal shift of magnitude |b/2a| units.The magnitude of the scaling depends upon the magnitude of a. If a is negative, the parabola will also flip its mouth from the positive to the negative side. Step 1: x 2 to ax 2: This will imply a vertical scaling of the original parabola.Now, to plot the graph of f(x), we start by taking the graph of x 2, and applying a series of transformations to it: Here, the vertex of the parabola is (h, k) = (-b/2a, -D/4a). The term D is the discriminant, given by D = b 2 - 4ac. First, we rearrange it (by the method of completion of squares) to the following form: f(x) = a(x + b/2a) 2 - D/4a. Consider the general quadratic function f(x) = ax 2 + bx + c. We will study a step-by-step procedure to plot the graph of any quadratic function. Graphing Quadratic Functions in Vertex Form ![]()
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