Question

Write the steps in transforming a quadratic equation to it's standard form

Answer 1

Answer:

Its simple. Steps below.

Step-by-step explanation:

Transforming Quadratic Functions from General Form to Standard...

General Form f(x) = ax2 + bx + c.

Standard Form f(x) = a (x - h)2 + k.

Transforming Quadratic Functions from General Form to Standard Form.

f(x) = ax2 + bx + c Step 1: Factor out a from the first two terms. ...

Step 2: Complete the square. ...

Step 3: Factor and combine.

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Answer 2

Given: a quadratic equation ax^2+bx+c =0

To find: Steps to convert it into standard form

Solution: the given quadratic equation is ax^2+bx+c=0 and we have to convert it into the standard form of a quadratic equation and that is an (x-h)^2 +k

so for that first, we need to make a perfect square that is (x-h)^2 and for that, we need to make the coefficient of x^2 = 1

so we can write the given equation as

an ( x^2 + bx/a + c/a)

and to write it in a perfect square we form it as

a(( x+b/2a)^2 +u)

here u will be found as

b^2/4a +au = c

u = c/a - b^2/4a^2

so the equation can be written as

an ( x+ b/2a)^2 + (c/a - b^2/4a^2)

it is in the form of an (x-h)^2/+k

here h = -b/2a and k = c/a - b^2/4a^2

Therefore, the quadratic equation in standard form is

Therefore, the quadratic equation in standard form is an ( x+ b/2a)^2 + (c/a - b^2/4a^2).