How do you write in standard form #y=3/4(x-4)^2+2#?

1 Answer
Oct 29, 2016

The standard form of this quadratic function is #y = 3/4x ^2 - 6x + 14#.

Explanation:

Standard form of a quadratic function is #y = ax^2 + bx + c#. To transform this quadratic function from vertex form to standard form, begin by squaring the binomial. Remember the process of squaring a binomial:

#(a + b)^2#
#(a + b)(a + b)#
#a^2 + ab + ab + b^2#
#a^2 + 2ab + b^2#

So applying this process to #y = 3/4(x - 4)^2 + 2# gives us:

#y = 3/4(x^2 - 8x + 16) + 2#

Now, distribute the coefficient #3/4#:

#y = 3/4x^2 - 6x + 12 + 2#

Combine the constants:

#y = 3/4x^2 - 6x + 14#

This is the standard form of the quadratic function.