The form ax2 + bx + c = 0 is called standard form of a quadratic equation. Before solving a quadratic equation using the Quadratic Formula, it's vital that you be sure the equation is in this form. If you don't, you might use the wrong values for a, b, or c, and then the formula will give incorrect solutions.
ExampleProblemRewrite the equation 3x + 2x2 + 4 = 5 in standard form and identify a, b, and c. 3x + 2x2 + 4 = 53x + 2x2 + 4 – 5 = 5 – 5First be sure that the right side of the equation is 0. In this case, all you need to do is subtract 5 from both sides. 3x + 2x2 – 1 = 02x2 + 3x – 1 = 0Simplify, and write the terms with the exponent on the variable in descending order. 2x2+3x–1=0↓ ↓ ↓ ax2 bx c a = 2, b = 3, c = −1 Now that the equation is in standard form, you can read the values of a, b, and c from the coefficients and constant. Note that since the constant 1 is subtracted, c must be negative.Answer2x2 + 3x – 1 = 0; a = 2, b = 3, c = −1
ExampleProblemRewrite the equation 2(x + 3)2 – 5x = 6 in standard form and identify a, b, and c. 2(x + 3)2 – 5x = 62(x + 3)2 – 5x – 6 = 6 – 6First be sure that the right side of the equation is 0. 2(x2 + 6x + 9) – 5x – 6 = 02x2 + 12x + 18 – 5x – 6 = 02x2 + 12x – 5x + 18 – 6 = 02x2 + 7x + 12 = 0Expand the squared binomial, then simplify by combining like terms. Be sure to write the terms with the exponent on the variable in descending order. 2x2+7x+12=0↓ ↓ ↓ a b c a = 2, b = 7, c = 12 Now that the equation is in standard form, you can read the values of a, b, and c from the coefficients and constant.Answer2x2 + 7x + 12 = 0; a = 2, b = 7, c = 12
Identify the values of a, b, and c in the standard form of the equation 3x + x2 = 6. A) a = 3, b = 1, c = 6B) a = 1, b = 3, c = 6C) a = 1, b = 3, c = −6D) a = 3, b = 1, c = −6 Show/Hide Answer
