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The curve above represents a parabola, it has an x-intercept of -1 and y-intercept of 2.  Find the area of the square.

 

 Jun 15, 2020
 #1
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If it is a square centered on the origin....     then   |x| = |y|.  At the corner that intercepts the parabola.....compute the formula of the parabola first.....then......

 Jun 15, 2020
 #2
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The graph touches the x-axis at only 1 point. This means the equation of the graph must be a product of a perfect square and a real constant, in this case:

 

\(y = k(x + 1)^2\)

 

When x = 0, y = 2.

 

\(2=k\cdot 1^2\\ k = 2\)

 

Therefore, the equation of the parabola is \(y = 2(x + 1)^2\).

 

If it is a square with one of the vertices being the origin, then two of the vertices lies on |y| = |x|, in this case, two of the vertices lies on y = -x.

 

We solve the system of simultaneous equations

 

\(\begin{cases}y = 2(x + 1)^2\\y = -x\end{cases}\)

 

I will leave the rest for you.

 Jun 15, 2020

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