How Do You Find the a, b, and c Values of a Quadratic Function?

Remember, the standard form of a quadratic looks like ax²+bx+c, where 'x' is a variable and 'a', 'b', and 'c' are constant coefficients
Knowing 'a', 'b', and 'c' helps you solve quadratic equations!
When a coefficient is missing in front of a variable, you know that it's just equal to 1 :)
'c' is the constant term in the quadratic equation because it's not attached to an 'x' variable
An equation without an x² is not a quadratic equation, it's linear

1. Remember, the standard form of a quadratic looks like ax²+bx+c, where 'x' is a variable and 'a', 'b', and 'c' are constant coefficients
2. ax² is called the quadratic term, bx is the linear terms, and c is the constant term
1. Knowing 'a', 'b', and 'c' helps you solve quadratic equations!
2. The 'a' value is the coefficient in front of 'x²'
3. In a quadratic equation, 'a' can't be zero! If it is zero, then you lose your quadratic term :)
1. Knowing 'a', 'b', and 'c' helps you solve quadratic equations!
2. The 'b' value is the coefficient in front of 'x'
1. 'c' is the constant term, the term that doesn't contain x raised to some non-zero power
2. Watch out for tricks! You could write c = c•x⁰, since x⁰=1!
1. Let's look at what happens when 'a', 'b', and 'c' take on special values!
1. To make y=12x+32 look like ax²+bx+c, you need to make a=0, b=12, c=32. But 'a' can't be zero in standard quadratic form, since 'a'=0 turns the equation into a linear equation!
2. If you don't see an x² term, you don't have a quadratic equation!
1. In the case of y=x²+32, a=1, c=32, and there is no 'x' term. That means that 'b' just equals 0!
1. In the case of y=x²+12x, a=1, b=12, and there is no constant term. That means that 'c' just equals 0!

Identify the a, b, and c values of y = x2 + 12x + 32.