How do you plot a quadratic function in JavaScript?

Use the equation y = ax² + bx + c to calculate y values for each x, then plot them using the Canvas API or SVG.

Can you animate a parabola in JavaScript?

Yes. By updating x values over time and redrawing the curve, you can visualize parabolic motion or projectile paths dynamically.

What does the coefficient 'a' control in a quadratic function?

The coefficient 'a' determines the direction and width of the parabola. A positive 'a' opens upward, while a negative 'a' opens downward.

Solving and Animating a Quadratic Equation in JavaScript

Understanding the Quadratic Function | Maths Explanation for JavaScript Kids

In this tutorial, we'll explore how to solve quadratic equations in JavaScript and use them to plot and animate a quadratic curve on an HTML5 canvas. Understanding the quadratic equation in programming helps you create parabolic motion, simulations, and engaging math visuals.

A quadratic equation has the general form y = ax² + bx + c; where a, b, and c are constants. This tutorial explains how to solve, plot, and animate a quadratic function using JavaScript and the HTML5 canvas element.

Figure: JavaScript graph of quadratic curve

Generating Quadratic Curves for JavaScript

To generate a quadratic curve in JavaScript, you need two points - the starting point and the vertex (turning point - maximum or minimum).

Figure: Quadratic equation graph in JavaScript showing quadratic points - start point and turning (maximum) point.

The general quadratic function is:

y = ax² + bx + c

^dy/_dx = y^I = 2ax + b
At maximum / minimum point, y^I = 0
y^I|_{(x = x_max)} = 0
2ax_max + b = 0
b = -2ax_max

Substituting b in the general equation
y = ax² + bx + c
  = ax² - 2ax_maxx + c

         At (x_start, y_start):
y_start = ax_start² - 2ax_maxx_start + c
         At (x_max, y_max):
y_max = ax_max² - 2ax_max² + c
    = -ax_max² + c     --------- (eqn *)

Subtracting both derived equations
y_start - y_max = ax_start² - 2ax_maxx_start + ax_max²
(x_start² - 2x_maxx_start + x_max²)a = y_start - y_max

Hence:

a =	y_start - y_max	=	y_start - y_max
	x_start² - 2x_maxx_start + x_max²		(x_start - x_max)²

b = -2ax_max
& from (eqn *)
c = y_max + ax_max²

JavaScript Code Example: Quadratic Path Animation

Once we have the equation, we can generate a quadratic curve with JavaScript to visualize its motion. The following example demonstrates how to animate an object along a quadratic curve in JavaScript using the HTML5 canvas. This is a simple form of quadratic motion simulation that helps visualize parabolic motion, such as a ball being thrown.

To make a body travel by the equation of a quadratic curve, continuously increment x by some interval, and use the quadratic equation to get the corresponding y value.

Create a new file; On Notepad++: File, New.
Call it quadratic_path.html.
Type out the adjoining JavaScript code for animating an image body through the path of a quadratic curve.
This simple example demonstrates JavaScript quadratic animation.

Key Takeaways on Quadratic Path Animation in JavaScript

A quadratic function in JavaScript models parabolic motion or curves.
The quadratic equation JavaScript code can be used for plotting and animations.
The constants a, b, and c control the shape and direction of the parabola.

Applications in JavaScript Programming and STEM Education

The quadratic equation in JavaScript is useful for programming concepts like projectile motion, trajectory planning, and smooth animation curves. Teachers can use this example to show how maths and coding connect - making parabolas come alive through JavaScript programming.

Teachers and students can use this JavaScript quadratic formula tutorial to explore math and programming together. It's a practical example of using maths with code.

Summary: Visualizing Quadratic Equations in JavaScript

In this tutorial, you've learnt how to solve quadratic equations in JavaScript using the quadratic formula. We've also explore how to plot and animate a quadratic curve on an HTML5 canvas. Understanding how to code the quadratic equation in JavaScript is useful for creating simulations, parabolic motion, and smooth animations.

By combining mathematics and JavaScript, you can solve and animate quadratic equations easily. Whether you're plotting parabolas, simulating motion, or building educational tools, mastering the quadratic formula in JavaScript gives you a solid foundation in computational math.

So! JavaScript Fun Practice Exercise - Animate along Quadratic Path

As a fun practice exercise, try adjusting the coefficients a, b, and c to change the curve's shape or motion pattern. This will be a great way to connect mathematics and programming, and help you understand more about JavaScript animations and quadratic equations.

JavaScript Animation Code for quadratic_path.html

<!DOCTYPE html>
<html lang="en">
    <head>
        <title>Quadratic Track</title>
    </head>
    <body>

        <h3>Move in the Trajectory of a Quadratic Curve</h3>

        <canvas id="move_quad" width="500" height="300" style="border: 1px solid #000000;">
            Your browser (version) does not support canvas object; Time to update!
        </canvas>
        <button onclick="moveQuadratic()">Move</button>

        <script>
            var canvas = document.getElementById("move_quad");
            var context = canvas.getContext("2d");
            context.fillStyle = "#888888"; // color for our moving body(circle)

            var x_start = 50;
            var y_start = 200;
            var x_max = 200;
            var y_max = 50;
            var x = x_start;
            var y = y_start;
            // draw a dot
            context.beginPath();
            context.arc(x, y, 5, 0, 2 * Math.PI);
            context.fill();

            // constants
            var a = (y_start - y_max) / Math.pow((x_start - x_max), 2);
            var b = -2 * a * x_max;
            var c = y_max + a * Math.pow(x_max, 2);
            var x_stop = 350;
            function moveQuadratic() {
                // condition for continuing motion
                if (x <= x_stop) {
                    y = a * x * x + b * x + c;

                    // redraw dot
                    context.beginPath();
                    context.arc(x, y, 5, 0, 2 * Math.PI);
                    context.fill();

                    x += 20;
                    setTimeout(function () { moveQuadratic(); }, 100);
                }
            }
        </script>

    </body>
</html>

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