Question

Graph the equation y=-x^2-2x+3 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Answer 1

See below (along with attached graph)

5th point can be of personal choice

Explanation:

X-intercepts/Roots

`y=-x^2-2x+3\\\\0=-x^2-2x+3\\\\0=-(x^2+2x-3)\\\\0=-(x+3)(x-1)\\\\x=-3,\: x=1\\\\(-3,0)\:and\:(1,0)`

Y-intercept

`y=-x^2-2x+3\\\\y=-(0)^2-2(0)+3\\\\y=3\\\\(0,3)`

Vertex

`x=-(b)/(2a)\\ \\x=-((-2))/(2(-1))\\ \\x=(2)/(-2)\\ \\x=-1\\\\y=-x^2-2x+3\\\\y=-(-1)^2-2(-1)+3\\\\y=-1+2+3\\\\y=4\\\\(-1,4)`