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Answer:
a) f(x) = -2x² + 4x
Explanation:
To find the standard form we need to solve the equation as:
So, the standard form is f(x) = -2x² + 4x
To make the graph we will use the initial form because when the equation is written like f(x) = a(x-h)²+k, the coordinate (h,k) is the vertex of the parabola
So, in this case, the vertex of the parabola is the point (1, 2)
On the other hand, we can find a point in the graph. For example, if x is equal to 0, then f(x) is equal to:
f(x) = -2(x-1)² + 2
f(0) = -2(0-1)² + 2
f(0) = -2(-1)² + 2
f(0) = - 2 + 2
f(0) = 0
So, the parabola passes through the point (0,0) and has a vertex in the point (1, 2). Then, the graph is:
