Which is the correct answer?

We have three points (-1,2), (2,-4), (4,2)

The right way to do this problem is just plug in x=-1 into each equation and check that y=2.  For any equation that worked for that one try the other two points.  I'll do it differently, in a way that doesn't assume we have a menu of choices to choose from.

In general we can work out three equations in three unknowns.  But there's a shortcut here because we see two equal y values.  As we know the parabola is bilaterally symmetric, symmetric via reflection on its axis.  Since we have these equal y values we know the axis is right in the middle, x=(-1+4)/2 = 3/2.

So instead of an arbitrary three variable y=ax²+bx+c we can capture the symmetry and go right to

y = a(x-3/2)² + c

Let's plug in the first two points,

2 = a(-1 - 3/2)² + c = (25/4)a + c

-4 = a(2 - 3/2)² + c = (1/4)a + c

Subtracting,

6 = (24/4)a = 6a

a = 1

-4 = (1/4) + c

c = -17/4

y =  (1)(x-3/2)² + -17/4

y = x² - 3x + 9/4 - 17/4

y = x² - 3x - 2

Choice I

answer: when you burn wood, the carbon reacts with the oxygen in the air to create ash and smoke. that is a permanent change you cannot undo that.

step-by-step explanation:

whatvare the choices

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