Vertex and axis intercepts

Text

For the parabola $y=x^{2}+2x-8$, find the vertex and the axis intercepts.

Solution

Vertex abscissa: $x_V=-\dfrac{b}{2a}=-1$; ordinate: $y_V=1-2-8=-9$, i.e. $V(-1,-9)$. $x$-intercepts: $x^{2}+2x-8=(x+4)(x-2)=0\Rightarrow x=-4,\ x=2$. $y$-intercept: $y(0)=-8$. $\boxed{\,V(-1,-9),\quad (-4,0),\ (2,0),\quad (0,-8)\,}$