(c) Find its maximum or minimum value.
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The standard form of a quadratic function is
where (h, k) is the vertex of the parabola.
f(x) can be expressed in standard form by completing the square.
First make the coefficient of x^2 1 by taking -1 common
Take half of coefficient of x which gives 3/2
and square it which gives (3/2)^2 = 9/4
Add and subtract 9/4 from the equation inside the bracket.
This is the standard form of the quadratic function.
Since a = -1 < 0, the parabola opens downwards.
Hence the vertex is the highest point on the parabola.
Vertex = (h, k) = (-3/2, 21/4)
So, maximum value = 21/4
b) Maximum value is f(x) = 21/4
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