College algebra . FlQ. 11. Abts. 50,51] QUADRATIC FUNCTIONS 71 For we have shown that every quadratic equation has two roots,real or imaginary. If the curve has no point in common withthe X-axis, there is no real root of the equation. Hence hothroots are imaginary. If the curve touches the X-axis, both rootsof the equation are real and equal. These three cases are shownin Fig. 11, where the graphs oi a? — 2x-3, a:^ — 2k +1, andx^ — 2x + 6 are given. EXERCISES Construct the graphs of the functions in the following equations, and, bymeasurement, determine the roots if they are real. Calculate th
College algebra . FlQ. 11. Abts. 50,51] QUADRATIC FUNCTIONS 71 For we have shown that every quadratic equation has two roots,real or imaginary. If the curve has no point in common withthe X-axis, there is no real root of the equation. Hence hothroots are imaginary. If the curve touches the X-axis, both rootsof the equation are real and equal. These three cases are shownin Fig. 11, where the graphs oi a? — 2x-3, a:^ — 2k +1, andx^ — 2x + 6 are given. EXERCISES Construct the graphs of the functions in the following equations, and, bymeasurement, determine the roots if they are real. Calculate the value ofthe function for at least ten values of x between the limits given. Choosethe vertical unit so that the graph vriU be of convenient proportions for thecoordinate paper. 1. a;2 — 5a; + 4 = 0, from a = 0 to a; = 5. 2. a;2 + a; — 6 = 0, from a; = — 4 to a; = 3. 3. 4x2 + 12x + 5 = 0, from x = — 4 to x = 1. 4. x2 — 3 X = 0, from x = — 1 to x = 4. 5. x2 + 2x + 2 = 0, from x =— 3 to x = 2. 6
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