Question

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

Answer 1

Answer:

is a function

Step-by-step explanation:

the x coordinate do not repeat themselves

Answer 2

Answer:

See below

Step-by-step explanation:

X-intercepts / Zeroes / Roots:

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

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

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-2\pm\sqrt{2^2-4(-1)(6)}}{2(-1)}$

$x=\frac{-2\pm\sqrt{4+24}}{-2}$

$x=\frac{-2\pm\sqrt{28}}{-2}$

$x=\frac{-2\pm2\sqrt{7}}{-2}$

$x=1\pm\sqrt{7}$

$(1+\sqrt{7},0)$ and $(1-\sqrt{7},0)$

Y-intercept:

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

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

$f(0)=6$

$(0,6)$

Vertex:

$x=-\frac{b}{2a}$

$x=-\frac{2}{2(-1)}$

$x=\frac{-2}{-2}$

$x=1$

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

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

$f(1)=1+6$

$f(1)=7$

$(1,7)$

Domain:

$(-\infty,\infty)$

Range:

$(\infty,7)$