# How do you graph y = -x^2 - 4x - 3?

Apr 21, 2015

To start with the basic idea, this is a quadratic function with a negative leading term. It would therefore represent a vertical parabola, opening downward. Rewrite it in the following form:
y=$- {x}^{2} - 4 x - 3$
=$- {x}^{2} - 4 x - 4 + 1$
= -${\left(x + 2\right)}^{2}$+1

This shows the vertex of the parabola (-2,1) and the axis of symmetry x=-2.

The graph would have two x intercepts, given by $- {x}^{2} - 4 x - 3 = 0$, that is (x+1)(x+3)=0; x= -1, -3

The graph would have one y intercept given by y=-3.

Mark all the points given above on a graph and sketch the symmetrical figure of parabola on either side of the axis of symmetry.