algebra

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what is the equation in standard form of a parabola that contain the following points?
(-2,-20),(0,-4),(4,-20)

• algebra -

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

• algebra -

Thanks for helping I have posted two other questions if you might be able to help

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