Question

How do you find the axis of symmetry, graph and find the maximum or minimum value of the function `y = x^2 - 2x - 10`?

Answer 1

Complete the square

Explanation:

In this case, completing the square would give you:

`y=(x-1)^2-11`

Once in this form `y=(x-p)^2+q`, the negative of p is the x coordinate of the vertex of the graph and q is the y coordinate. This means the minimum (as the coefficient of `x^2` is positive (1)) of the graph will be at ( 1 , -11 ) and the line of symmetry will pass through the x coordinate, namely `x = 1`

Answer 2

Axis of symmetry: `x=1`; minimum value `-11`

Explanation:

graph{x^2-2x-10 [-28.52, 29.22, -14.43, 14.45]}

A quadratic equation in standard form is `y=ax^2+bx+c`. In this case, `a=1`, `b=-2`, and `c=-10`.
To find the axis of symmetry, use the formula `x=-b/(2a)`.

`x=-b/(2a)`
`x=-(-2)/(2(1))`
`x=1`

The graph above shows that the parabola is an upward-facing one, so it has a minimum value. The max or min is always on the axis of symmetry, so you can substitute `x=1` into the function.

`y=x^2-2x-10`
`y=1^2-2(1)-10`
`y=-11`

So, the axis of symmetry is `x=1` and the minimum value is `-11`. You can also write the minimum as the coordinate `(1,-11)`.