Question

What is the vertex of `y= x^2- 6x + 14`?

Answer 1

(3, 5)

Explanation:

The x-coordinate of the vertex of a parabola is given by `-b/(2a)`. Remember that parabolas in standard form are `ax^2+bx+c`. With this in mind, we can see that, for our parabola, `a = 1`, `b = -6`, and `c = 14`.

To find the x-coordinate of the vertex, we just plug in the value of `a` and `b` into `-b/(2a)`:

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

Now that we have the `x`, we plug it into our parabola to find `y`:

`(3)^2-6(3)+14 = 9-18+14 = 5`

Our y-coordinate is 5, meaning our vertex is the point (3,5).