There are two roots. One of them is $0$, and it is most convenient to let the other equal $2b$ for some $b>0$.

Then the equation of the parabola must be of the form

for some $a>0$.

Focus on this triangle first. Get $h$ in terms of $a$ and $b$, then use Pythagoras.

Now use this triangle to get a second equation in $a$, $b$ and $d$.

There are two roots. One of them is $0$, and it is most convenient to let the other equal $2b$ for some $b>0$.

Then the equation of the parabola must be of the form

for some $a>0$. The coefficient of $x^2$ will be $-a$ - this is what we're looking for.

Let's focus on this triangle first:

The height $h$ of the triangle is given by $y$ when $x=b$:

Then, by Pythagoras,

Next, let's look at this triangle

Again by Pythagoras, we have

We can equate these two expressions for $d^2$ to find that

However, $a>0$ and $b>0$, so $ab=1$.

Going back now to the equation of the parabola, we have

So the coefficient of $x$ is $2$.