Question

How do you find the vertex of `y = x^2 – 10x + 5`?

Answer 1

The formula for x coordinate, h, of the vertex of a parabola described by an equation of the form `y=ax^2+bx +c` is:
`h = -b/(2a)`
The y coordinate, k, is found by evaluating the function at `x = h`.

Explanation:

Given: `y = x^2 – 10x + 5`

By observation, `a = 1, b = -10 and c = 5`

The x coordinate of the vertex is:

`h = -(-10)/(2(1))`

`h = 5`

Obtain the y coordinate, k, by evaluating the function at `x = 5`:

`k = 5^2 – 10(5) + 5`

`k = 25-50+5`

`k = -20`

The vertex is the point `(5,-20)`.