What is the equation of a parabola that passes through (-2,2), (0,1), and (1, -2.5)?

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What is the equation of a parabola that passes through (-2,2), (0,1), and (1, -2.5)?

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Answer 1 · 2018-05-08T08:08:29

See explanation below

Explanation:

A general parabola is like $a x^{2} + b x + c = f (x)$ $ax^2+bx+c=f(x)$
We need to "force" that this parabola passes thru these points. How do we do?. If parabola passes through these points, their coordinates acomplishes the parabola expresion. It say

If $P (x_{0}, y_{0})$ $P(x_0,y_0)$ is a parabola point, then $a x_{0}^{2} + b x_{0} + c = y_{0}$ $ax_0^2+bx_0+c=y_0$

Apply this to our case. We have

1.- $a {(- 2)}^{2} + b (- 2) + c = 2$ $a(-2)^2+b(-2)+c=2$
2.- $a \cdot 0 + b \cdot 0 + c = 1$ $a·0+b·0+c=1$
3.- $a \cdot 1^{2} + b \cdot 1 + c = - 2.5$ $a·1^2+b·1+c=-2.5$

From 2. $c = 1$ $c=1$
From 3 $a + b + 1 = - 2.5$ $a+b+1=-2.5$ multiply by 2 this equation and add to 3
From 1 $4 a - 2 b + 1 = 2$ $4a-2b+1=2$

$2 a + 2 b + 2 = - 5$ $2a+2b+2=-5$
$4 a - 2 b + 1 = 2$ $4a-2b+1=2$

$6 a + 3 = - 3$ $6a+3=-3$ , then $a = - 1$ $a=-1$

Now from 3... $- 1 + b + 1 = - 2.5$ $-1+b+1=-2.5$ give $b = - 2.5$ $b=-2.5$

The the parabola is $- x^{2} - 2.5 x + 1 = f (x)$ $-x^2-2.5x+1=f(x)$

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What is the equation of a parabola that passes through (-2,2), (0,1), and (1, -2.5)?

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Explanation:

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