Question

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

Answer 1

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 -4x -3`
=`-x^2 -4x -4+1`
= -`(x+2)^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^2-4x-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.