curriculum/challenges/english/blocks/learn-interfaces-by-building-an-equation-solver/6650f037c017aa6855a608e3.md
The graph of any quadratic equation has a parabolic shape. The \( x \) coordinate of the vertex of the parabola can be found at \( x = - \frac{b}{2a} \).
From the analyze method, return the dictionary containing two keys, 'x', and 'y', and the corresponding values of the vertex \( x \) and \( y \) coordinates, respectively.
Use the relation above to find the \( x \) coordinate. Then, use the \( x \) coordinate to calculate the \( y \) coordinate.
You should return a dictionary containing two keys, 'x', and 'y', and the corresponding values of vertex x and y coordinates, respectively.
({ test: () => runPython(`
eq = QuadraticEquation(16, 2, 1)
assert eq.analyze() == {'x': -0.0625, 'y': 0.9375}
`) })
from abc import ABC, abstractmethod
import re
class Equation(ABC):
degree: int
def __init__(self, *args):
if (self.degree + 1) != len(args):
raise TypeError(
f"'Equation' object takes {self.degree + 1} positional arguments but {len(args)} were given"
)
if any(not isinstance(arg, (int, float)) for arg in args):
raise TypeError("Coefficients must be of type 'int' or 'float'")
if args[0] == 0:
raise ValueError("Highest degree coefficient must be different from zero")
self.coefficients = {(len(args) - n - 1): arg for n, arg in enumerate(args)}
def __init_subclass__(cls):
if not hasattr(cls, "degree"):
raise AttributeError(
f"Cannot create '{cls.__name__}' class: missing required attribute 'degree'"
)
def __str__(self):
terms = []
for n, coefficient in self.coefficients.items():
if not coefficient:
continue
if n == 0:
terms.append(f'{coefficient:+}')
elif n == 1:
terms.append(f'{coefficient:+}x')
else:
terms.append(f"{coefficient:+}x**{n}")
equation_string = ' '.join(terms) + ' = 0'
return re.sub(r"(?<!\d)1(?=x)", "", equation_string.strip("+"))
@abstractmethod
def solve(self):
pass
@abstractmethod
def analyze(self):
pass
class LinearEquation(Equation):
degree = 1
def solve(self):
a, b = self.coefficients.values()
x = -b / a
return [x]
def analyze(self):
slope, intercept = self.coefficients.values()
return {'slope': slope, 'intercept': intercept}
class QuadraticEquation(Equation):
degree = 2
def __init__(self, *args):
super().__init__(*args)
a, b, c = self.coefficients.values()
self.delta = b**2 - 4 * a * c
def solve(self):
if self.delta < 0:
return []
a, b, _ = self.coefficients.values()
x1 = (-b + (self.delta) ** 0.5) / (2 * a)
x2 = (-b - (self.delta) ** 0.5) / (2 * a)
if self.delta == 0:
return [x1]
return [x1, x2]
--fcc-editable-region--
def analyze(self):
pass
--fcc-editable-region--
lin_eq = LinearEquation(2, 3)
print(lin_eq)
quadr_eq = QuadraticEquation(1, 2, 1)
print(quadr_eq)
print(quadr_eq.solve())