is actually acquired utilizing the steps connected in completing the square. It stems from the reality that any quadratic feature or equation of the develop y = ax^2 + bx + c deserve to be addressed for its roots. The “roots” of the quadratic equation are the points at which the graph of a quadratic function (the graph is called the parabola) hits, crosses or touches the x-axis well-known as the x-intercepts.

You are watching: What does it mean to derive an equation

So to find the roots or x-intercepts of y = ax^2 + bx + c, we have to let y = 0. That indicates we have

ax2 + bx + c = 0

From here, I am going to use the usual measures involved in completing the square to arrive at the quadratic formula.

Steps on How to Derive the Quadratic Formula

Derivation of the quadratic formula is easy! Here we go.

Tip 1: Let y = 0 in the basic develop of the quadratic attribute y = ax^2 + bx + c where a, b, and also c are actual numbers but a e 0.

Tip 2:Move the constant colorredc to the appropriate side of the equation by subtracting both sides by colorredc .

Tip 3:Divide the whole equation by the coreliable of the squared termwhich is largea.

Tip 4:Now identify the coeffective of the direct term largex.

Step 5:Divide it by 2 and raise it to the 2nd power. Then simplify it additionally.

Tip 6:Add the output of step #5 to both sides of the equation.
Tip 8:Expush the trinomial on the left side of the equation as the square of a binomial.
Step 9:Take the square root of both sides of the equation to eliminate the exponent 2 of the binomial.
Tip 10:Simplify. Make sure that you connect the colorred pm on the right side of the equation. The left side no longer consists of the power 2.
Step 11:Keep the variable x on the left side by subtracting both sides by Largeb over 2a.

See more: Why Did Forrest Gump Wear Leg Braces ? Why Did Forest Gump Need Leg Braces

Step 12:Simplify and also we are done!

I hope that youfind the step-by-action solution helpful infiguring out exactly how the quadratic formula is derivedutilizing the approach of completing the square.

You can be interested in:

The Quadratic Formula

ABOUTAbout MeSitemapContact MePrivacy PolicyCookie PolicyTerms of Service
MATH SUBJECTSIntroductory AlgebraIntermediate AlgebraCutting edge AlgebraAlgebra Word ProblemsGeometryIntro to Number TheoryBasic Math Proofs
We usage cookies to provide you the ideal endure on our webwebsite. Please click Ok or Scroll Down to usage this website via cookies. Otherwise, inspect your web browser settings to turn cookies off or discontinue making use of the site.OK!Cookie Policy