Question

At the skateboard park, the hot new attraction is the U-Dip, a cement structure embedded into the ground. The cross-sectional view of the U-Dip is a parabola that dips 15 feet below the ground. The width at ground level, its widest part is 40 feet across. Sketch the cross-sectional view of the U-Dip, and find an equation of the parabola that models it.

What is the a value as a decimal without rounding for your equation?

Answer 1

The equation for the parabola modeling the U-Dip skateboard park structure is y=0.0375x^2 - 15, with an a value of 0.0375.

Step-by-step explanation:

The student is tasked with sketching the cross-sectional view of a U-Dip skateboard park structure and finding an equation for the parabola that models it. The structure's cross section is 40 feet wide at the ground level and dips 15 feet below ground at its vertex.

Since the parabola is symmetrical and its vertex is the lowest point, we can place the vertex at the origin (0,0) of a coordinate system for convenience. The parabola will open upwards. To find the equation of this parabola in the form y=a(x-h)^2+k, where (h,k) is the vertex of the parabola, we can use the given dimensions of the U-Dip. We have h=0 and k=-15 because the vertex is placed at the origin and the parabola dips 15 feet below ground level. The width of the parabola at the ground level is 40 feet, so we find the point (20,0), which is 20 feet to the right of the vertex and at ground level.

Substituting this point into the equation y=a(x-0)^2-15, we get 0=a(20)^2-15. Solving for a, we get a=15/400, which simplifies to a=0.0375.

So, the equation of the parabola is y=0.0375x^2 - 15, and the a value as a decimal without rounding for this equation is 0.0375.