General Form. Standard Form(Vertex Form) where a,b, and c are real numbers, with. where a, h, and k are real numbers, with.
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1 Quadratic Equations A quadratic equation is a second degree polynomial equation in x. Meaning that there is at least one term that is being squared and there is NO exponent in the equation that is greater than 2. A quadratic equation in is an equation that can be written in several forms in this unit we will cover the two most common forms the general form and the standard form(vertex form).
2 General Form where a,b, and c are real numbers, with. Standard Form(Vertex Form) where a, h, and k are real numbers, with.
3 No matter which form we can see that a quadratic equation the degree is 2.(review the wording) or The degree just means the highest exponent of a polynomial equation in one variable.
4 The letters a, b, and c can be any real number with one exception. The letter a(leading coefficient) can never equal to zero. or The leading coefficient is the number in front of the variable with the highest exponent.
5 No matter how the terms are arranged in the equation the following will always be true. a is always the number in front of the x 2 term. b is always the number in front of the x term. c is the term that does not have a variable. QUADRATIC LINEAR CONSTANT
6 Given the equation :, identify the values of a,b, and c. SOLUTION The important thing to notice here is that terms in the equation are not aligned with the definition of the general form of a quadratic equation.
7 No matter how the terms are arranged in the equation the following will always be true. a is always the number in front of the x 2 term. b is always the number in front of the x term. c is the term that does not have a variable.
8 Another option is too rewrite the equation so that it is aligned with the definition of the general form of the quadratic equation. QUADRATIC LINEAR CONSTANT Identify the quadratic term, linear term, and the constant term. CONSTANT QUADRATIC LINEAR
9 Rewrite the equation in the following order : QUADRATIC LINEAR CONSTANT Now that the equation is aligned with the general form equation we see that
10 Given either form of the equation what is the reason the letter? or
11 SOLUTION Set a = 0. Zero times any value is zero, this simplifies to the following. If you add zero to any value it remains the same now the equation simplifies to the following.
12 Recall that the definition of a quadratic equation is any second degree polynomial equation in one variable. Meaning that there is at least one term that is being squared and there is NO exponent in the equation that is greater than 2. Notice in the equation : bx + c = 0, which is equivalent to the following :. The highest exponent is 1 which means the equation is a linear equation not a quadratic equation.
13 Comprehension Questions 1. A quadratic equation is a degree polynomial equation. For problems 2 4 determine whether the equation is a quadratic equation. If the equation is not a quadratic equation state the reason why it is not.
14 5. Given the equation : the 3, is the coefficient. 6. Given the equation :, state the linear term :. 7. Given the equation :, state the quadratic term :. 8. Given the equation :, state the constant term :.
15 9. Given the equation of the general form of a quadratic equation which coefficient is in front of the x term. 10. Given the equation :, state the values of a =, b =, and c =. 11. Given the equation :, state the values of a =, b =, and c =. 12. Given the equation :, state the values of a =, b =, and c =.
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