How can PHP be used to calculate and visualize mathematical functions like parabolas?

To calculate and visualize mathematical functions like parabolas using PHP, we can use mathematical formulas to generate the points on the curve and then plot them on a graph. This can be achieved by calculating the y-coordinate for a given x-coordinate using the formula for a parabola (y = ax^2 + bx + c) and then plotting these points on a graph using a library like GD. 

<?php

// Set the coefficients for the parabola
$a = 1;
$b = 2;
$c = 1;

// Define the range of x values
$x_min = -10;
$x_max = 10;

// Create an image canvas
$width = 800;
$height = 600;
$image = imagecreatetruecolor($width, $height);
$bg_color = imagecolorallocate($image, 255, 255, 255);
$line_color = imagecolorallocate($image, 0, 0, 0);

imagefill($image, 0, 0, $bg_color);

// Plot the parabola
for ($x = $x_min; $x <= $x_max; $x += 0.1) {
    $y = $a * pow($x, 2) + $b * $x + $c;
    $plot_x = $width / 2 + $x * 20;
    $plot_y = $height / 2 - $y * 20;
    imagesetpixel($image, $plot_x, $plot_y, $line_color);
}

// Output the image
header('Content-type: image/png');
imagepng($image);
imagedestroy($image);

?>

Keywords

PHP mathematical functions parabolas visualization graphing

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