The Quadratic Formula

One of my favourite formulas that I have learned in math recently is the quadratic formula. The quadratic formula is used to find the x-intercepts of a quadratic function; an equation that looks like a “U” shape on a graph. A quadratic function usually comes in two different equations: standard form as y=ax^2+bx+c or vertex form as y=a(x-h)^2+k. Yet, only equations written in standard form can be used with the quadratic formula. The quadratic formula is written as follows: y=-b+(or)-√b^2-4*a*c/2a (everything after the “√b” to the “c” is under the square root). So, the numbers that represent a, b, and c in the standard form of a quadratic equation are substituted as the same values in the quadratic formula. Also, if the quadratic equation has two x-intercepts, then two forms of the quadratic formula are used to find each x-intercept. One equation has a “+” before the square root, and the other has a “-” before the square root. Or, if an equation only has one x-intercept for whatever reason, both equations of the quadratic formula should calculate to find the same solution.

Moreover, if one wished to determine if a quadratic equation has one, two, or zero x-intercepts, a shorter version of the quadratic formula can be used instead: √b^2-4ac (the whole thing is under the square root). In this case, if the solution is greater than 1 then the equation has multiple x-intercepts, if the solution is equal to 0 than the equation has 1 x-intercept, and if the equation is a negative square root than the equation has no x-intercepts because negative square roots are mathematically impossible to solve.

So, there you have it! A thorough explanation of the quadratic formula– my favourite formula– in a few simple paragraphs. You’re welcome!

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