Sketch the graph of $y=(2+x)(x-6)$ on the axes below. Indicate clearly the values where the graph crosses the axes and write down the equation of the line of symmetry. Answer line of symmetry: ...

1. Find the points where the graph crosses the $x$-axis

At the $x$-axis, $y=0$.

$(x+2)(x-6)=0$

So $x=-2$ or $x=6$.

The graph crosses the $x$-axis at $(-2,0)$ and $(6,0)$.

2. Find the point where the graph crosses the $y$-axis

At the $y$-axis, $x=0$.

$y=(0+2)(0-6)=2(-6)=-12$

The graph crosses the $y$-axis at $(0,-12)$.

3. Find the line of symmetry and describe the sketch

The line of symmetry is halfway between the two $x$-intercepts.

$x=\frac{-2+6}{2}=2$

Since

$(x+2)(x-6)=x^2-4x-12,$

the coefficient of $x^2$ is positive, so the parabola opens upwards. Sketch a U-shaped curve through $(-2,0)$, $(6,0)$ and $(0,-12)$, with vertical line of symmetry $x=2$.