Question

find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x,y) point. y=x²- 2x-6

Answer 1

Answer:

(1, -7)

Explanations:

If a parabola is of the form:

`y\text{ = a(x - h)}^2+k`

The vertex of the parabola is (h, k)

The given equation is:

`y=x^2-2x-6`

The given equation can be written in the form y = a(x-h)²+k

`\begin{gathered} y=x^2-2x-6 \\ y=(x-1)^2-7 \end{gathered}`
`\begin{gathered} \text{Comparing y = (x-1)}^2-7withy=a(x-h)^2+k \\ h\text{ = 1, k = -7} \end{gathered}`

The coordinates of the vertex are (1, -7)