The image contains a math question related to quadratic functions. Let's break down the two questions:

For question 693: The function provided is $y = 2x^2 + 8x + 6$, and the problem asks which explanation is correct regarding its graph. The options are:

1. The graph passes through all quadrants.
2. The axis of symmetry is $x = 2$.
3. The vertex of the graph is $(2, -2)$.
4. The graph intersects the x-axis at $(1, 0)$ and $(3, 0)$.
5. The equation is the same as $y = -2x^2 - 8x - 6$.

To find the correct option:

• The vertex of the parabola is given by $x = -\frac{b}{2a}$, where the general form is $y = ax^2 + bx + c$.
• For the given equation, $a = 2$, $b = 8$, and $c = 6$.
• The vertex is at $x = -\frac{8}{2(2)} = -2$.
• Substituting $x = -2$ into the equation to find $y$, we get: $y = 2(-2)^2 + 8(-2) + 6 = 2(4) - 16 + 6 = 8 - 16 + 6 = -2$ So, the vertex is $(-2, -2)$, and the axis of symmetry is $x = -2$, not $x = 2$.

Therefore, the correct option should be the one that reflects the vertex $(-2, -2)$.

For question 694: The function is $y = 3x^2 - 12x + 4$, and we are asked to find $k$ such that the graph moves in the direction where $x$ is increasing when $y$ is increasing.

To solve for $k$, the axis of symmetry for this quadratic equation is found similarly by the formula $x = -\frac{b}{2a}$. Here:

• $a = 3$, $b = -12$, and $c = 4$.
• The axis of symmetry is at $x = -\frac{-12}{2(3)} = 2$.

The graph will open upwards because $a = 3 > 0$, and the direction of motion will be increasing in the positive $x$-direction for increasing $y$.

The value $k$ refers to the coefficient that would result in this behavior for $y$.

Let me know if you'd like further clarification or solutions!