Difference between revisions of "Graph a Quadratic Equation"
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When graphed, quadratic equations of the form '''ax<sup>2</sup> + bx + c ''' or '''a(x - h)<sup>2</sup> + k''' give a smooth U-shaped or a reverse U-shaped curve called a ''parabola.'' Graphing a quadratic equation is a matter of finding its vertex, direction, and, often, its x and y intercepts. In the cases of relatively simple quadratic equations, it may also be enough to plug in a range of x values and plot a curve based on the resulting points. See Step 1 below to get started. | When graphed, quadratic equations of the form '''ax<sup>2</sup> + bx + c ''' or '''a(x - h)<sup>2</sup> + k''' give a smooth U-shaped or a reverse U-shaped curve called a ''parabola.'' Graphing a quadratic equation is a matter of finding its vertex, direction, and, often, its x and y intercepts. In the cases of relatively simple quadratic equations, it may also be enough to plug in a range of x values and plot a curve based on the resulting points. See Step 1 below to get started. | ||
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== Steps == | == Steps == | ||
#Determine which form of quadratic equation you have. The quadratic equation can be written in three different forms: the standard form, vertex form, and the quadratic form. You can use either form to graph a quadratic equation; the process for graphing each is slightly different. If you're doing a homework problem, you'll usually receive the problem in one of these two forms - in other words, you won't be able to choose, so it's best to understand both. The two forms of quadratic equation are: | #Determine which form of quadratic equation you have. The quadratic equation can be written in three different forms: the standard form, vertex form, and the quadratic form. You can use either form to graph a quadratic equation; the process for graphing each is slightly different. If you're doing a homework problem, you'll usually receive the problem in one of these two forms - in other words, you won't be able to choose, so it's best to understand both. The two forms of quadratic equation are: | ||
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#** Plot these points to the graph and draw your U-shaped curve. Note that the parabola is perfectly symmetrical - when your points on one side of the parabola lie on whole numbers, you can usually save yourself some work by simply reflecting a given point across the parabola's axis of symmetry to find the corresponding point on the other side of the parabola. | #** Plot these points to the graph and draw your U-shaped curve. Note that the parabola is perfectly symmetrical - when your points on one side of the parabola lie on whole numbers, you can usually save yourself some work by simply reflecting a given point across the parabola's axis of symmetry to find the corresponding point on the other side of the parabola. | ||
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== Tips == | == Tips == | ||
