Question

What is the vertex and the equation of the axis of symmetry of the graph of y=x2-6x-7?

Answer 1

x= -b over 2a = --6 over 2×1=3
y=3²-6(3)-7=-16
vertex is (3,-16)
axis of symmetry is 3

Answer 2

The vertex is (3,-16) and axis of symmetry is 3

Explanation:

The vertex of a quadratic equation
`f(x)=ax^(2)+bx+c` is calculated as
`((-b)/(2a),f((-b)/(2a)))`

and the axis of symmetry is
`(-b)/(2a)`

Compare equation
`y=x^(2)-6x-7` with
`f(x)=ax^(2)+bx+c`

Where a= 1 and b = -6

so,
`x=(-b)/(2a)=(-(-6))/(2)`

`x=3`

Now, put the value of x=3 in
`y=x^(2)-6x-7`

`y=(3)^(2)-6(3)-7`

`y=9-18-7`

`y=-16`

Therefore, the vertex is (3,-16) and axis of symmetry is 3