Posted by Lee on Monday, October 29, 2012 at 3:54pm.
you can probably save some time by looking at the points. You know that parabolas are symmetric, so, since y(-2) = y(4), the axis of symmetry is at x=(-2+4)/2 = 1.
So, with x=1 the axis of symmetry (and hence at the vertex), you will have
y = a(x-1)^2+k
at x=0, y= -4, so
-4 = a+k
-20 = 9a + k
k=-2
a=-2
so, y = -2(x-1)^2 - 2
or, y = -2x^2 + 4x - 4
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or, if you let y = ax^2 + bx + c,
-20 = 4a - 2b + c
-4 = c
-20 = 16a + 4b + c
a = -2
b = 4
c = -4
y = -2x^2 + 4x - 4
Thanks for helping I have posted two other questions if you might be able to help