# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function #y=-x^2+3x-3#?

Axis of symmetry

As this is in the form of

the axis of symmetry is at

So axis of symmetry is at

. I will let you work that out!

We already know that

So the point

As P is a maximum and below the x-axis then we also know that that it does not cross the x-axis. So there is no solution to

To emphasise the point:

In the solution equation:

The part:

giving:

As we are dealing with the sqrt of a negative number this is a sure sign that the graph does not cross the x-axis.

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To find the axis of symmetry, use the formula x = -b / (2a), where a = -1 (coefficient of x^2) and b = 3 (coefficient of x).

Substitute these values into the formula: x = -3 / (2 * (-1)) x = -3 / -2 x = 3/2

To graph the function, plot points or use a graphing calculator. The graph will be a parabola opening downwards.

To find the maximum or minimum value, note that the parabola opens downwards, so it has a maximum value. This occurs at the vertex, which is also the axis of symmetry.

Substitute x = 3/2 into the equation to find the y-coordinate of the vertex: y = -(3/2)^2 + 3(3/2) - 3 y = -9/4 + 9/2 - 3 y = -9/4 + 18/4 - 12/4 y = -3/4

So, the maximum value of the function is -3/4.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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