Section 8.4

# Section 8.4 - ax 2 bx c = 0 3 Try factoring 4 If factoring...

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Section 8.4 The Quadratic Formula 1

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The Quadratic Formula 2 2 The solutions of 0, a 0, are given by 4 2 ax bx c b b ac x a + + = - ± - = 2
The Discriminant: b 2 – 4ac Discriminant Nature of Solutions 0 One Solution; a rational number Positive Perfect Square Not a Perfect Square Two real-number solutions. Solutions are rational. Solutions are irrational. Negative Two imaginary-number solutions (complex conjugates) 3

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For each equation, a) Evaluate the discriminant b) How many and what type of solutions exist? C) Support your answer graphically. 2 2 2 2 1) 9 24 16 0 3) 4 8 2) 6 5 4 0 4) 3 5 7 x x x x x x a a - + = + = + - = + = 4
To Solve a Quadratic Equation 1) If the equation can be easily written in the form ax 2 = p or (x + k) 2 = d, use the principle of square roots. 2) If step 1 does not apply, write the equation in the form

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Unformatted text preview: ax 2 + bx + c = 0. 3) Try factoring. 4) If factoring seems too difficult or impossible, use the quadratic formula. Completing the square can also be used. The solutions of a quadratic equation can always be found using the quadratic formula. They cannot always be found by factoring. 5 Solve using the quadratic formula. ( 29 ( 29 2 2 2 1) 7 3 2) 9 4 3) 7 2 5 3 1 1 1 1 4) 2 4 2 x x x x x x x x x x x +- = + = + + = +-+ = 6 The current in a typical Mississippi River shipping route flows at a rate of 4 mph. In order for a barge to travel 24 mi upriver and then return in a total of 5 hr, approximately how fast must the barge be able to travel in still water? 7...
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Section 8.4 - ax 2 bx c = 0 3 Try factoring 4 If factoring...

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