(c) Find its maximum or minimum value.

Thank you for the opportunity to help you with your question!

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

ANSWER:

a)

b) Maximum value is f(x) = 21/4

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