Question

The inside walls of a bowl are designed to have cross-sections in the shape of a parabola. The width of the bowl at its opening is 23 centimeters and the depth of the bowl is 13 centimeters. Assuming that the base of the bowl is represented by the point (0,0), which of the following gives the equation of the parabola that can be used to model the walls of the bowl

Answer 1

Answer:

y= 0.0983x²

Step-by-step explanation:

The general equation of parabola is:

y= ax² + bx +c

since base of bowl is (0,0) or origin, the x intercept is 0 and y intercept is 0

The equation of parabola becomes

0= a(0)²+ b(0) +c

c=0

y= ax² + bx ----------- Eq I

at y= 13, x=-11.5, 11.5

substituting above values in Eq I

13= a(11.5)² + b(11.5)

13=132.25a + 11.5 b ---------------- Eq II

13= a(11.5)² + b(-11.5)

13=132.25a - 11.5 b ---------------- Eq III

Solving Eq II and Eq III simultaneously gives

a= 0.0983  b=0

Equation of parabola becomes

y= 0.0983x²