Question 11
A piecewise linear function is defined by $$
f(x) = \begin{cases} x & \text{if } -1 \le x \lt 1 \\ 2 - x & \text{if } 1 \le x \lt 3 \end{cases}
$$ and $f(x + 4) = f(x)$ for all real numbers $x.$ The graph of $f(x)$ has the sawtooth pattern depicted below.
The parabola $x = 34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of all these intersection points can be expressed in the form $\frac{a + b\sqrt{c}}{d},$ where $a,$ $b,$ $c,$ and $d$ are positive integers such that $a,$ $b,$ $d$ have greatest common divisor equal to $1,$ and $c$ is not divisible by the square of any prime. Find $a + b + c + d.$
f(x) = \begin{cases} x & \text{if } -1 \le x \lt 1 \\ 2 - x & \text{if } 1 \le x \lt 3 \end{cases}
$$ and $f(x + 4) = f(x)$ for all real numbers $x.$ The graph of $f(x)$ has the sawtooth pattern depicted below.
The parabola $x = 34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of all these intersection points can be expressed in the form $\frac{a + b\sqrt{c}}{d},$ where $a,$ $b,$ $c,$ and $d$ are positive integers such that $a,$ $b,$ $d$ have greatest common divisor equal to $1,$ and $c$ is not divisible by the square of any prime. Find $a + b + c + d.$