It appears you've uploaded an image containing a set of math questions related to the intersection of a line and a parabola. I will analyze the image and provide detailed insights.

Let me first break down the question:

• The given line equation is $y = -3x - m + 2$ and the parabola equation is $y = x^2$.
• The problem asks about different scenarios where the line and parabola intersect.

I'll provide solutions for the given sub-questions, starting with:

a) $m > \frac{17}{4}$, and the question asks if the line intersects the parabola at two distinct points.

To determine the intersection points between the line and parabola, we need to set the equations equal to each other:

$-3x - m + 2 = x^2$

Rearrange the equation:

$x^2 + 3x + (m - 2) = 0$

Now, we apply the discriminant from the quadratic formula to check how many real solutions there are (which corresponds to the number of intersection points). The discriminant $\Delta$ is given by:

$\Delta = b^2 - 4ac$

For our equation $x^2 + 3x + (m - 2) = 0$, we have $a = 1$, $b = 3$, and $c = m - 2$. Thus, the discriminant is:

$\Delta = 3^2 - 4(1)(m - 2) = 9 - 4(m - 2) = 9 - 4m + 8 = 17 - 4m$

For the line and the parabola to intersect at two distinct points, the discriminant must be positive:

$17 - 4m > 0$

Solving for $m$:

$4m < 17 \quad \Rightarrow \quad m < \frac{17}{4}$

Therefore, if $m > \frac{17}{4}$, the discriminant becomes negative, meaning no real solutions exist. So, the line will not intersect the parabola at two distinct points.

Thus, the answer to part (a) is "Sai" (False).

Let me know if you want detailed steps for the other sub-questions (b), (c), or (d) as well!