How to solve Quadratic Equations By John Jackson.

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Presentation transcript:

How to solve Quadratic Equations By John Jackson

Solving by Graphing F(x) = x 2 + 3x + 1 XY Type the equation into the Calculator to see where the graph Crosses the x axis Create X/Y graph or 

Solving by Factoring X 2 + 5x + 6 = 12 X 2 + 5x – 6= 0 (x + 6)(x – 1) = 0 X + 6 = 0 x – 1 =0 x = -6 x = 1 Set the equation equal to zero By subtracting 12 from both sides. Factor so that the 2 numbers add To the linear term, but multiply The constant term. Set both parentheses equal to zero And solve for x.

Solving by Completing the Square X 2 + 6x + 2 = 0 X 2 + 6x = -2 X 2 + 6x + 9 = (x + 3) 2 = 7 X + 3 = ± √ 7 X = -3 ± √ 7. Move the constant term to the RHS by Subtracting 2 to both sides Find the perfect square trinomial by Taking half of the linear term, square it, Then add it to both sides Factor the LHS and simplify the RHS Take the square root of both sides Solve for x by 3 by both sides

Solving by the Quadratic Formula X 2 – 4x – 8 = 0 X = -(-4) ±√(-4)2 – 4(1)(- 8) 2(1) = 4 ± √ = 4 ± √ = 4 ± √ 3 * 16 = 4 ± 4 √3 2 2 = 2(2 ± 2 √3) = 2 ± 2 √3 2 X = 2 ± 2 √3 Solve for the discriminant First b 2 – 4ac Substitute all numbers, and Discriminant into the Quadratic formula x = -b±√b2-4ac 2a Simplify if you can.