. College algebra, with applications. tly that a quadratic function appears ina more complicated form than (1), owing to the fact thatvarious terms, which might be united into a single one, arewritten separately. When such an expression is rewrittenin the form (1), we say that it has been reduced to itsstandard form. EXERCISE XIX Reduce the following quadratic functious of x to the standard form,and indicate the values of a, h, and c in each case. 1. 5 X + 4 - .3 x2. 2. 2 a:^ + a; - .5 X- - 4 X + 7. 3. mx + ix2 + 3 r/x - 4 + d. 4. (mx + ky^ + x- - r^. 65. Graph of a quadratic function. The met
. College algebra, with applications. tly that a quadratic function appears ina more complicated form than (1), owing to the fact thatvarious terms, which might be united into a single one, arewritten separately. When such an expression is rewrittenin the form (1), we say that it has been reduced to itsstandard form. EXERCISE XIX Reduce the following quadratic functious of x to the standard form,and indicate the values of a, h, and c in each case. 1. 5 X + 4 - .3 x2. 2. 2 a:^ + a; - .5 X- - 4 X + 7. 3. mx + ix2 + 3 r/x - 4 + d. 4. (mx + ky^ + x- - r^. 65. Graph of a quadratic function. The method used inArt. 52 for making the graph of a linear function may alsobe applied to a quadratic function. But the graph will notbe a straight line. The curved graph obtained by plottinga quadratic function is called a parabola. The followingexamples will serve to make the student familiar with theform of this curve. 94 Art. 65] GRAPH OF A QUADRATIC FUNCTION 95 % li -4 + 16 -;3 + 9 _ 2 + 4 - 1 + 1 0 0 + 1 + 1 + 2 + 4 + ;3 + ;) + 4 + 16. Fig. EXERCISE XX 1. Construct the graph of the func-tion X-. Solution. We put y = x-, and assignto X arbitrary values, such as — 4, — 3,- 2, - 1, 0, + 1, + 2, +3, +4, etc. We compute the corre-sponding values of y and obtain in this way the pairs of numbers indicated in the table. Each of these pairs of numbers we regard as the coordinates of a point, indicated in Fig. 35 by a little cross. Finally we join these points by a smooth curve. Observe that the curve has a lowestpoint or minimum at (0, 0), and that thecurve i^ symmetric with respect to the //-axis. The point O is called the vertex of the parabola, and the axis ofsymmetry (the ^/-axis in this case) is called its axis. 2. Draw the graphs oi y = 2 x^, y — o ofi, y — \ ^^i y = \ ^ ^^^ com-pare with the graph oiy — x^ as obtained in Ex. 1. For the purposes ofthis comparison it is desirable to draw these five curves on the samesheet, referred to the same coordinate axes. 3. Draw the
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