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How do you graph quadratic equations?

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Quick Answer

The simplest way to graph a quadratic equation is to substitute an array of values for x in the equation and solve for y in each case to obtain several (x,y) coordinates. After obtaining the coordinates, they can be plotted on graph paper along the x-y axis to form a parabolic curve that is typical of a quadratic equation.

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A quadratic equation has an x^2 function in it and is typically represented in a y=ax^2 + bx + c format. When graphing along the x-y axis, the coordinates on the graph should form a parabolic curve that is drawn without using a ruler, so the curve is smooth and doesn't comprise linear segments.

Another method of plotting is to first find the vertex of the parabolic curve. The x coordinate of the vertex is found using the equation (-b/2a), and the y coordinate of the vertex is determined by substituting the x coordinate in the quadratic equation and solving it. The vertical plane of the vertex forms the line of symmetry between the two sides of the curve. The rest of the x coordinates are chosen from either side of the x coordinate of the vertex, and the corresponding y values are obtained by solving the equation.

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