Question

State the y-intercept,x-intercepts, and vertex in point form (solutions need only)x2= power to 2 y=-x2 -6x-8

Answer 1

`y=-x^2-6x-8`

y-intercept -> x=0

`\begin{gathered} y=-0^2-6\cdot0-8 \\ y=-0-0-8 \\ y=-8 \end{gathered}`

y-intercept -> x=0, then: (0,-8)

x-intercept -> y=0

`\begin{gathered} y=-x^2-6x-8 \\ \Delta=36-32=4 \\ x=\frac{6\pm\sqrt[]{4}}{-2}=(6\pm2)/(-2) \\ x_1=(8)/(-2)=-4 \\ x_2=(4)/(-2)=-2_{} \end{gathered}`

x-intercept -> y=0, then: (-2,0) e (-4,0)

vertex

`x_v=-(b)/(2a)=-(6)/(-2)=-3`

now find yv

`\begin{gathered} y_v=-(-3)^2-6\cdot(-3)-8 \\ y_v=-9+18-8=9-8=1 \end{gathered}`

vertex= (-3,1)

The graph below shows the x-intercept and y-intercept