Homework. Graph the quadratic functions in standard form (1.1)

Question

Graph the function by hand. Y=x^2-4x+3

Answer 1

x^2 -4x +3

take the derivative, set =0

2x -4 =0

x = 2 is the x coordinate of the quadratic's vertex

y coordinate is (2)^2 -4(2) +3 = 4-8+3 =-1

vertex = (2,-1) = minimum point of an upward opening parabola

x^2 -4x +4 = -3+4 =1

complete the square

(x-2)^2 -1 is in vertex form where (h,k) = vertex of (x-h)^2 +k, (h,k) =(2,-1)

(x-2)^2 =1

x -2 = + or -1

x= 2+or-1 = 3 or 1 = x intercepts, y intercept =3= constant term