(a) Express f in standard form.

Question

f(x) = x² − 2x + 6

Answer 1

f(x) = x^2 -2x + 6

= x^2 -2x +1 + 6 -1

= (x-1)^2 + 5 in vertex form, with vertex = (1,5)= minimum point

it's an upward opening parabola with axis of symmetry x=1

with y intercept = 6 or the point (0,6)

vertex form is considered "standard form" for a quadratic function

f(x) = a(x-h)^2 + k where (h,k) = vertex = minimum point when a>0

if a<0, then the vertex is the maximum point

if a=0, the "quadratic" collapses into a linear flat horizontal equation y=k

x = 2/2 +/- (1/2)sqr(4-24) = the two imaginary x intercepts

=1 +/-.5isqr20

=1+2isqr5, 1+2isqr5

the parabola never touches or intersects the x axis,

so there are no real x intercepts

f(x) = (x-1-2isqr5)(x-1+2isqr5) in factored form