A small API that can give information about a quadratic equation, including vertex, zeros, y-intercept, and coefficients.

quadratic.js

// Parse a quadratic, find its coefficients, and feed it into the "quadratic" function
function parseQuadratic(input) {
  const refined = input.toLowerCase().replaceAll(" ", "");
  
  // A regex that matches and finds the coefficients in a quadratic in the format ax^2+bx+c
  const matches = refined.match(/(-?[0-9.]*)[a-z]\^2(?:([+-][0-9.]*)[a-z])?([+-][0-9.]*)?/)
    .slice(1) // We don't want the first value (which is the full match)
    .map(str => Number( // we will convert our refined coefficients from a string to a number
      (str ?? "0") // If the current item in the matches list is undefined, it was not provided, the coefficient will be 0
      .replace(/^[+-]?$/, x => x + "1"))); // If we have only +/- or even no coefficient along with the x, we assume it is 1
  return quadratic(...matches); // Apply our coefficients to the "quadratic" function
}

// Generate statistics about a quadratic equation, including zeros, vertex, coefficients, and more
function quadratic(a, b, c) {
  return {
    zeros: [(-b + Math.sqrt(b**2 - 4*a*c)) / (2*a), (-b - Math.sqrt(b**2 - 4*a*c)) / (2*a)],
    vertex: [-b / (2*a), a * (-b / (2*a))**2 + b * (-b / (2*a)) + c],
    yIntercept: c,
    mirrorX: -b / (2*a),
    coefficients: [a, b, c],
    discriminant: b**2-4*a*c,
    valueAt(x) {
      // Applies the quadratic to any x value
      return a * (x**2) + b*x + c;
    }
  }
}

console.log(parseQuadratic(prompt("Enter a quadratic in the form of ax^2+bx+c"))); // Prompt the user