Answer:
The vertex is (3,-16) and axis of symmetry is 3
Step-by-step explanation:
The vertex of a quadratic equation [tex]f(x)=ax^{2}+bx+c[/tex] is calculated as [tex](\frac{-b}{2a},f(\frac{-b}{2a}))[/tex]
and the axis of symmetry is [tex]\frac{-b}{2a}[/tex]
Compare equation [tex]y=x^{2}-6x-7[/tex] with [tex]f(x)=ax^{2}+bx+c[/tex]
Where a= 1 and b = -6
so, [tex]x=\frac{-b}{2a}=\frac{-(-6)}{2}[/tex]
[tex]x=3[/tex]
Now, put the value of x=3 in [tex]y=x^{2}-6x-7[/tex]
[tex]y=(3)^{2}-6(3)-7[/tex]
[tex]y=9-18-7[/tex]
[tex]y=-16[/tex]
Therefore, the vertex is (3,-16) and axis of symmetry is 3
