Question 229600
Determine the solutions of{{{7-6x-x^2 = 0}}} by graphing.
First, the solutions to this quadratic equation are found where the curve (a parabola) intersects the x-axis.
Second, if the coefficient of the {{{x^2}}}term is positive, the parabola opens upwards and the function has a minimum. If the coefficient is negative, as it is in this case, then the parabola opens downwards and the function has a maximum. 
Let's look at the graph of this function:
{{{graph(400,400,-10,5,-5,20,7-6x-x^2)}}}
Notice that the parabola intersects the x-axis in two places so there are two solutions (also called roots). The maximum occurs at (-3, 16)
{{{highlight(x = -7)}}} and {{{highlight(x = 1)}}}