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Writing Quadratic Equations in Standard Form ax2 + bx + c = 0 and Finding the Values of a, b, and c
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Writing Quadratic Equations in Standard Form ax2 + bx + c = 0 and Finding the Values of a, b, and c
1.
Writing Quadratic Equation
in the Form of ax2 + bx + c = 0, and Finding the Value of a, b, and c.
2.
Example 1. x2
= 5 – 2x ax2 + bx + c = 0 x2 = 5 – 2x x2 + 2x – 5 = 0 a = 1, b = 2, c = -5
3.
Example 2. -11x
+ 4 = 2x2 – x - 5 ax2 + bx + c = 0 -11x + 4 = 2x2 – x - 5 = 2x2 – x + 11x – 5 – 4 (simplify) 0 = 2x2 + 10x – 9 a = 2, b = 10, c = -9 remember: (An equation ax2 + bx + c = 0 is the same as 0 = ax2 + bx + c.)
4.
Example 3. 3x2
= 36 ax2 + bx + c = 0 3x2 = 36 3x2 – 36 = 0 a = 3, b = 0, c = -36
5.
Example 4. (x
+ 2)2 = -6 + 3x ax2 + bx + c = 0 (x + 2)2 = -6 + 3x x2 + 4x + 4 = -6 + 3x x2 + 4x – 3x + 4 + 6 = 0 x2 + x + 10 = 0 a = 1, b = 1, c = 10
6.
Example 5. 11
= 3x + x2 ax2 + bx + c = 0 11 = 3x + x2 0 = x2 + 3x – 11 a =1, b = 3, c = -11
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