Question

How do you find the intercept and vertex of `y = x^2 – 4x + 9`?

Answer 1

The minimum value of this expression (the vertex) is at the point (2,5). The graph never touches the x axis but it intercepts the y-axis at the point (0,5)

Explanation:

Rewrite the equation using completing the squares.
`y = x^2 - 4x +4 - 4 + 9`
`y = (x - 2)^2 -4 +9`
`y = (x-2)^2 +5`

The minimum value of this expression (the vertex) is when x = 2 at the point (2,5). The graph never touches the x axis but it intercepts the y-axis at the point (0,5)