1. The problem provides two quartic functions and their graph transformations. 2. First function: $y = \frac{5}{4}x^4 + 3$. - This is a quartic function $y = x^4$ scaled vertically by $\frac{5}{4}$ (stretching the graph). - Shifted vertically upward by 3 units. - Since the coefficient of $x^4$ is positive, the graph opens upward with its minimum at $x=0$. 3. Second function: $y = -(x + 8)^4$. - The inner term $(x+8)$ shifts the graph horizontally to the left by 8 units. - The negative sign in front reflects the quartic function across the x-axis. - This graph opens downward with a maximum at $x = -8$. 4. Summary of transformations: - For $y=\frac{5}{4}x^4 +3$: vertical stretch by $\frac{5}{4}$, vertical shift up by 3. - For $y=-(x+8)^4$: reflection across x-axis, horizontal shift left by 8. 5. Both functions maintain the quartic shape (U-shaped for positive leading coefficient, inverted U-shaped for negative). Final functions: $$y=\frac{5}{4}x^4 + 3$$ $$y=-(x+8)^4$$