To find the horizontal distance \( x \) from the jumping platform where the skater is at their minimum height, we need to determine the vertex of the parabola represented by the equation \( y = 0.25x^2 - 4x + 19 \).
For a quadratic equation of the form \( ax^2 + bx + c \), the \( x \) value of the vertex (which represents the minimum or maximum point) can be calculated using the formula:
\[ x = -\frac{b}{2a} \]
In our equation, the coefficients are:
- \( a = 0.25 \)
- \( b = -4 \)
- \( c = 19 \)
Substituting the values of \( a \) and \( b \) into the vertex formula:
\[ x = -\frac{-4}{2(0.25)} = \frac{4}{0.5} = 8 \]
Thus, the skateboarder is 8 feet away from the jumping platform when they are at their minimum height off the ground.