The $y$-intercept occurs when $x=0$. So we set $x=0$ and solve for $y$:
$0 = 2y^2 - 3y + 7$
This quadratic equation does not factor nicely, so we can use the quadratic formula:
$y = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(2)(7)}}{2(2)}$
$y = \frac{3 \pm \sqrt{9 - 56}}{4}$
$y = \frac{3 \pm \sqrt{-47}}{4}$
Since the discriminant is negative, the quadratic equation has no real solutions. Therefore, the graph of the parabola $x = 2y^2 - 3y + 7$ does not have any $y$-intercepts. So the answer is $\boxed{0}$.The answer is: 0
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
How many $y$-intercepts does the graph of the parabola $x = 2y^2 - 3y + 7$ have?

### Answer:
