MediumCalculusca-037

Extrema of Quadratic on Interval

Problem

Find the minimum and maximum values of f(x) = a*x^2 + b*x + c on the closed interval [lo, hi].

Check the endpoints and the vertex x = -b / (2*a) when the vertex lies inside the interval, then return [min_value, max_value]. For a == 0 the function is linear.

Hint

An extreme value on a closed interval occurs at an endpoint or at an interior critical point.

Test cases

case 1

in: [1,0,0,-1,2]

expected: [0,4]

case 2

in: [-1,2,0,0,3]

expected: [-3,1]

case 3

in: [0,2,1,-1,1]

expected: [-1,3]

case 4

in: [1,-4,4,0,1]

expected: [1,4]

case 5

in: [2,0,-8,-2,1]

expected: [-8,0]

Starter codePython

def quadratic_extrema(a, b, c, lo, hi):
    # Return [min_value, max_value]
    # Your code here
    pass

5 test cases · run your code against them in the editor