零点

---
> id: parabola

    x-coordinate-system(x-axis="-5,5,1" y-axis="-3,5,1")

{.text-center} `y =`${a}{a|1|-5,5,0.1} `x^2+`${b}{b|0|-5,5,0.1} `x+`${c}{c|0|-5,5,0.1}

import {CoordinateSystem, Step} from '../shared/types';


function q(a: number, b: number, c: number) {
  return (x: number) => (a * x * x + b * x + c);
}


function zeros(a: number, b: number, c: number) {
  const disc = b * b - 4 * a * c;
  if (disc < 0) return [];

  if (nearlyEquals(disc, 0, 0.1)) return [-b / (2 * a)];

  const x1 = (-b + Math.sqrt(disc)) / (2 * a);
  const x2 = (-b - Math.sqrt(disc)) / (2 * a);
  return [x1, x2];
}


export function parabola($step: Step) {
  const $chart = $step.$('x-coordinate-system') as CoordinateSystem;

  $step.model.watch((s: any) => {
    const fn = q(s.a, s.b, s.c);
    $chart.setFunctions(fn);
    $chart.drawPoints(zeros(s.a, s.b, s.c).map(p => new Point(p, fn(p))));
  });
}