How do I figure out the parts of a quadratic equation? What is the formula and the parts of it?
Answers
Step-by-step explanation:
As we'll see shortly, in order to solve a quadratic equation by the Quadratic Formula, we first need to have the quadratic equation in standard form, i.e., ax² + bx + c = 0, where a, b, and c are real numbers and a does not equal 0.
The Quadratic Formula is: x = [‒b ± √(b² ‒ 4ac)]/(2a). The a, b, and c in the Quadratic Formula match or correspond to the a, b, and c coefficients in the quadratic equation in standard form: ax² + bx + c = 0, and that's because the Quadratic Formula is derived from the quadratic equation. So, once you get the quadratic equation to be solved into standard form, it's just a simple matter of identifying the numerical values for a, b, and c from the equation and then substituting those values into the Quadratic Formula for the corresponding a, b, and c and then simplifying and solving for x.
EXAMPLE: Solve the quadratic equation x² + 5x + 6 = 0.
The equation is already in standard form, ax² + bx + c = 0, so we can easily see that our values for a, b, and c are: a = 1, b = 5, and c = 6. Now, substituting these values into the Quadratic Formula to solve for x, we have:
x = [‒b ± √(b² ‒ 4ac)]/(2a)
= [‒5 ± √(5² ‒ 4(1)(6))]/[2(1)]
= [‒5 ± √(25 ‒ 24)]/2
= [‒5 ± √1]/2
= [‒5 ± 1]/2
Therefore, our solutions for the given quadratic equation are:
x= [‒5 + 1]/2 = ‒4/2 = ‒2 and
x = [‒5 ‒ 1]/2 = ‒6/2 = ‒3
CHECK:
FOR x = ‒2:
x² + 5x + 6 = 0
(‒2)² + 5(‒2) + 6 = 0
4 ‒ 10 + 6 = 0
4 + 6 ‒ 10 = 0
10 ‒ 10 = 0
0 = 0
The reader should verify x = ‒3.