find the constants a, b and c such that or all values of x,

Question

3x^2 - 5x + 1 = a(x+b)^2 +c

also whats the coordinate of the minimum point??

thanks for the help

Answer 1

Y = 3x^2 _ 5x + 1.
Vertex Form: y = a(x - h)^2 + k,

a = 3 = coefficient of x^2.

h = Xv = -b / 2a = 5/6 = 0.833.

Substitute 5/6 for x in the given Eq:
K = Yv=3*(5/6)^2 - 5*5/6 + 1 = -1.083.

Vertex Form: Y = 3(x - 5/6)^2 - 1.083.

V(h , k)=V(0.833 , -1.083) = Lowest
point.

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