Question
Using a certain ramp at the skate park, a skater’s height off the ground, in feet, is modeled by the equation y=0.25x2−4x+19 , where x is the skater’s horizontal distance from the jumping platform. How far from the jumping platform is a skateboarder when they are at their minimum height off the ground?(1 point) ft.
Answers
GPT-4o mini
To find the distance from the jumping platform at the minimum height, we need to analyze the quadratic function given:
\[ y = 0.25x^2 - 4x + 19 \]
This quadratic equation is in the form \( ax^2 + bx + c \), where:
- \( a = 0.25 \)
- \( b = -4 \)
- \( c = 19 \)
Since the coefficient \( a \) is positive, the parabola opens upwards, indicating that it has a minimum point.
The x-coordinate of the vertex (which gives the horizontal distance from the jumping platform at the minimum height) can be found using the formula:
\[ x = -\frac{b}{2a} \]
Plugging in the values for \( a \) and \( b \):
\[ x = -\frac{-4}{2 \times 0.25} \]
\[ x = \frac{4}{0.5} \]
\[ x = 8 \]
Therefore, the skateboarder is **8 feet** away from the jumping platform when they are at their minimum height off the ground.
\[ y = 0.25x^2 - 4x + 19 \]
This quadratic equation is in the form \( ax^2 + bx + c \), where:
- \( a = 0.25 \)
- \( b = -4 \)
- \( c = 19 \)
Since the coefficient \( a \) is positive, the parabola opens upwards, indicating that it has a minimum point.
The x-coordinate of the vertex (which gives the horizontal distance from the jumping platform at the minimum height) can be found using the formula:
\[ x = -\frac{b}{2a} \]
Plugging in the values for \( a \) and \( b \):
\[ x = -\frac{-4}{2 \times 0.25} \]
\[ x = \frac{4}{0.5} \]
\[ x = 8 \]
Therefore, the skateboarder is **8 feet** away from the jumping platform when they are at their minimum height off the ground.