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: