Express the function in general form

Question

Express in general form

y=3(x+0.5)^2 +2

Answer 1

y= 3(x+1/2)^2 + 2

=3(x^2 + x + 1/4) + 2

= 3x^2 +3x + 3/4 + 8/4

= 3x^2 +3x + 11/4

standard form is y=ax^2 +bx + c

In this example, a=3 b=3 and c = 11/4 = 2 3/4 = 2.75

in general form you can solve for x with the quadratic formula

x = -3/6 + or - (1/6)sqr(9-33) which gives 2 imaginary solutions

x=-1/2 + or - (i/3)sqr6. plug either x solution into the original equation and y=0