Question

The function f(x)= -x^2+2x+6

Answer 1

See below

Explanation:

X-intercepts / Zeroes / Roots:

`f(x)=-x^2+2x+6`

`0=-x^2+2x+6`

`x=(-b\pm√(b^2-4ac))/(2a)`

`x=(-2\pm√(2^2-4(-1)(6)))/(2(-1))`

`x=(-2\pm√(4+24))/(-2)`

`x=(-2\pm√(28))/(-2)`

`x=(-2\pm2√(7))/(-2)`

`x=1\pm√(7)`

`(1+√(7),0)` and
`(1-√(7),0)`

Y-intercept:

`f(x)=-x^2+2x+6`

`f(0)=-(0)^2+2(0)+6`

`f(0)=6`

`(0,6)`

Vertex:

`x=-(b)/(2a)`

`x=-(2)/(2(-1))`

`x=(-2)/(-2)`

`x=1`

`f(1)=-(1)^2+2(1)+6`

`f(1)=-1+2+6`

`f(1)=1+6`

`f(1)=7`

`(1,7)`

Domain:

`(-\infty,\infty)`

Range:

`(\infty,7)`

Answer 2

is a function

Explanation:

the x coordinate do not repeat themselves