Describe how to derive the quadratic formula from a quadratic equation in standard form

Step-by-step explanation:

The standard form of a quadratic equation in x can be written as;

where a,b, and c are constants.

The first step is to subtract c on both sides of the equation;

The next step is to divide both sides of the equation by the constant a;

Next, we complete the square on the left hand side of the equation by determining another constant c as;

We then add this constant on both sides of the equation in order to complete the square on the L.H.S;

The expression on the L.H.S of the equation is now a perfect square and can be factorized to yield;

We then take square roots on both sides of the equation and simplify the expression on the R.H.S;

The final step is to make x the subject of the formula and a little simplification which will yield the quadratic formula;

Putting the expression on the R.H.S under a common denominator yields;

which is the quadratic formula

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.

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step-by-step explanation: