SOLUTION: derive all the properties of a quadratic function y=4x^2-3x+2? (with step by step solution please)

Question 932894: derive all the properties of a quadratic function y=4x^2-3x+2?
(with step by step solution please)

Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
y =ax^2 + bx + c = a(x -(-b/2a)^2) - a(-b/2a)^2 + c
...
y=4x^2-3x+2
-b/2a = -(-3)/2*4 = 3/8
y = 4(x- 3/8)^2 - 4(9/64) + 2
y = 4(x- 3/8)^2 - 9/16 + 2
y = 4(x- 3/8)^2 + 23/16
Parabola opening Upward: a = 4 > 0 and x = 3/8 the Line of Symmetry
........
V(3/8, 23/16)
4 = 1/4p, p = 1/16
....
F(3/8, 24/16)
Directrix is y = 22/16
........
the vertex form of a Parabola opening up(a>0) or down(a<0),

where(h,k) is the vertex and x = h is the Line of Symmetry ,
the focus is (h,k + p), With Directrix y = (k - p), a = 1/(4p)

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