Question

How do you find the axis of symmetry, graph and find the maximum or minimum value of the function `y = –x^2 + 6x – 1`?

Answer 1

The formula for finding the axis of symmetry is given by `-b / (2a)`

Therefore, we can find the axis of symmetry given the function.

`- 6 / (2(1))` = `-3`

So, the axis of symmetry is `x = -3` because it is a vertical line.

To find the minimum or maximum, we just find the value at that vertical line of symmetry since the max or min is ALWAYS at the axis of symmetry for a quadratic.

`y = -(-3)^2 + 6(-3) - 1`

`y = -9 - 18 - 1`
`y = -28`

So we have the min as `(-3, -28)`

to graph, just plug in some x values and find corresponding y values.