How do you find the roots, real and imaginary, of y= (x-3)^2+2 using the quadratic formula?

1 Answer
Alan P.
Nov 29, 2015

Expand the expression on the right side into standard form, then apply the quadratic formula.
In this case there will be two imaginary roots 2+-isqrt(5)

Explanation:

y=(x-3)^2+2

rArr y= 1x^2+(-4)x+9

which is an example of quadratic standard form: y=ax^2+bx+c
for which the roots are given by the quadratic formula
color(white)("XXX")x= (-b+1sqrt(b^2-4ac))/(-2a)

Which for our example becomes:
color(white)("XXX")x= (-(-4)+-sqrt((-4)^2-4(1)(9)))/(2(1))

color(white)("XXXX")= (4+-sqrt(16-36))/2

color(white)("XXXX")=(4+-2sqrt(-5))/2

color(white)("XXXX")=2+-isqrt(5)

Related questions
See all questions in Quadratic Formula
Impact of this question
1411 views around the world
You can reuse this answer
Creative Commons License