Writing quadratic equation
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The document provides 5 examples of writing quadratic equations in the standard form of ax^2 + bx + c = 0. Each example expresses a given equation in terms of x and then identifies the coefficients a, b, and c. For example 1, the equation x^2 = 5 - 2x is written as x^2 + 2x - 5 = 0, with a = 1, b = 2, c = -5. The examples demonstrate how to rearrange various equations involving x terms and constants into the standard quadratic form.
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This document discusses squaring binomial expressions. It provides three examples of squaring binomials of the form (x + a), showing that (x + a)2 = x2 + 2a*x + a2. Specifically, it squares (x + 3), (b - 5), and (m - 15) to get x2 + 6x + 9, b2 - 10b + 25, and m2 - 60m + 225 respectively.
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The property illustrated by the expressions 8 + [6 + (-7)] = (8+6) + (-7) and 12 + 6 = 18 is the associative property of addition.
If 4r + 20 (7h) =36, and r=5h, then 20h + 20 (7h) =36 illustrates substituting 5h for r in the original equation.
If x+4 = 15, then x+4 – 4 = 15 – 4 illustrates subtracting 4 from both sides of the original equation to isolate the variable x.
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Writing quadratic equation
- 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