Question

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

Answer 1

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).

Answer 2

Answer:

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

Step-by-step explanation: