Help creating equation for parabola word problem?

Question

The cables of a suspension bridge create a parabola. The towers are 600 feet apart and 80 feet tall. If the cable touches the road halfway between the towers, what is the height of the cable at a point 150 feet away from the center of the bridge?

So I know that you would use x^2 = 4ay and I thought that a would 150 as that is 1/4 of 600, but the equation doesn't work out correctly and the book says the answer should be 20.

What am I missing here?

Answer 1

Let the 'center' be at the point $(0,0)$. There the parabola reaches it's minimum, so the the equation is of the form : $y = ax^2$. You can determine $a$ by the value of the function at $300$. It is given to be $80$, so you have $a300^2 = 80$ or $a = \frac{80}{300^2}$. Now the height at the point $150$ feet away from the center is $y = \frac{80}{300^2}150^2 = 80 \frac{1}{4} = 20$.

Answer 2

Hint: Just write $y=kx^2$, and the point $(300,80)$ must lie on the parabola. That tells you an $x$ and $y$ that satisfy the equation, so you can find $k$.

Once that's done, find the $y$ corresponding to $x=150$.