Introduction
You guys must be familiar with quadratic equations, especially if you study Algebra. There are different ways that we could solve quadratic equations. We can solve it using factorization, completing the square, root of a square expression or number, and the quadratic formula. We will learn about the quadratic formula and learn how to prove it.The quadratic formula
X equals minus B plus and minus root of B squared minus four A C over two A
A quadratic equation
Application of the quadratic formula on the Quadratic equation
Lets take a quadratic equation for example:
Step one: What we did was that we wrote down the equation on the top.
Step two: We wrote down the quadratic formula and took the values of A,B,and C in our head.
A=2
B=-8
C=-24
Step three: We plugged in the values into the quadratic formula
Step four, five, six, and seven: We solved for the quadratic formula using our previous tools for order of operations.
Proof of the quadratic formula
This is the proof of the quadratic formula:
Step one: Write down the quadratic equation
Step two:Subtract C from both sides
Step three: Divide the whole equation by A
Step four: Simplify the equation
Step five: Complete the square by dividing B/A(Coefficient of x) by 2 and then squaring the quotient and then adding the total amount of that action to both sides to get a perfect square on left hand side(L.H.S).
Step six: Turn the L.H.S expression into a square or factorize it(the result will be the same), and simplify the right hand side(R.H.S).
Step seven: Take the square root of both sides
Step eight: simplify the R H S.
Step nine: subtract b/2a from both sides
Step ten: Order the answer accordingly
Hope this explanation helps
