Write the function in the form $ax^2+bx+c$. Identify $a$ and $b$ from $g(x)$.

For $y=ax^2+bx+c$, recall the formula for the $x$-coordinate of the vertex. Then carefully substitute your values of $a$ and $b$, paying close attention to negative signs.

In Desmos, type y = x^2 - 2x - 8 to graph the quadratic function.

Click or tap on the lowest point of the parabola (its turning point). Desmos will show the coordinates of this vertex; read off the $x$-coordinate shown there.

The function is $g(x)=x^2-2x-8$. This is a quadratic in standard form $ax^2+bx+c$ with:

• $a=1$
• $b=-2$
• $c=-8$ (though $c$ is not needed for the vertex's $x$-coordinate).

For a quadratic function in the form $y=ax^2+bx+c$, the $x$-coordinate of the vertex is given by the formula

We will apply this formula using the values of $a$ and $b$ from $g(x)$.

Substitute $a=1$ and $b=-2$ into $x=-\frac{b}{2a}$:

So, the $x$-coordinate of the vertex of the graph of $g$ is $1$.