suppose it costs 28 cents, 21 cents, and 16 cents per mile to drive at 10, 20, and 30 mph. Write the quadratic equation for this function.

Question

suppose it costs 28 cents, 21 cents, and 16 cents per mile to drive at 10, 20, and 30 mph. Write the quadratic equation for this function.

Answer 1

(1, 28), (2, 21) and (3, 16) = (10 mph, cents per mile)

plot the 3 points and find a quadratic that goes through them.

y = ax^2 + bx + c

28=a+b + c

21 =4a+2b + c

16 = 9a +3b + c

3 equations 3 unknowns

use elimination and substitution or matrix algebra

a=1, b=-10, c=37