Question

What is the vertex and x-intercepts of the graph of the function below
y=x^2-6x-7

Answer 1

x=(7,0),(-1,0) y=(0,-7)

Explanation:

Answer 2

Answer: The vertex is (3, 16) and the x-intercepts are (-1, 0) and (7, 0).

Step-by-step explanation: We are given to find the vertex and x-intercepts of the graph of the following function :

`y=x^2-6x-7~~~~~~~~~~~~~~~~~~~~~~~~~~~`(i)`

We know that

the vertex of the graph of function
`y=a f(x-h)^2-k` is given by (h, k).

From equation (i), we have

`y=x^2-6x-7\\\\\Rightarrow y=(x^2-6x+9)-7-9\\\\\Rightarrow y=(x-3)^2-16.`

Therefore, the vertex is (3, 16).

The x-intercepts of function (i) will be given by

`x^2-6x-7=0\\\\\Rightarrow x^2-7x+x-7=0\\\\\Rightarrow x(x-7)+1(x-7)=0\\\\\Rightarrow (x+1)(x-7)=0\\\\\Rightarrow x+1=0,~~x-7=0\\\\\Rightarrow x=-1,~~x=7.`

Thus, the vertex is (3, 16) and the x-intercepts are (-1, 0) and (7, 0).