The curve above represents a parabola, it has an x-intercept of -1 and y-intercept of 2. Find the area of the square.
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......
+9519 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.
