Graphing Calculator

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Graphing Calculator (Quadratic & Linear)
Quadratic: ax² + bx + cLinear: mx + b
Results: Enter values and click Calculate to see the properties of the function.
function toggleInputs(){var type=document.getElementById('funcType').value;if(type==='linear'){document.getElementById('rowB').style.display='none';document.getElementById('labelA').innerHTML='Slope (m):';document.getElementById('labelC').innerHTML='Y-Intercept (b):';}else{document.getElementById('rowB').style.display='table-row';document.getElementById('labelA').innerHTML='Coefficient a:';document.getElementById('labelC').innerHTML='Constant c:';}}function clearCanvas(){var canvas=document.getElementById('graphCanvas');var ctx=canvas.getContext('2d');ctx.clearRect(0,0,canvas.width,canvas.height);document.getElementById('results').innerHTML='Results: Enter values and click Calculate to see the properties of the function.';}function calculateGraph(){var type=document.getElementById('funcType').value;var a=parseFloat(document.getElementById('inputA').value);var b=parseFloat(document.getElementById('inputB').value);var c=parseFloat(document.getElementById('inputC').value);var canvas=document.getElementById('graphCanvas');var ctx=canvas.getContext('2d');var resDiv=document.getElementById('results');if(isNaN(a)||isNaN(c)||(type==='quadratic'&&isNaN(b))){resDiv.innerHTML='Please enter valid numeric coefficients.';return;}ctx.clearRect(0,0,canvas.width,canvas.height);var width=canvas.width;var height=canvas.height;var scale=20;ctx.beginPath();ctx.strokeStyle='#ccc';ctx.moveTo(0,height/2);ctx.lineTo(width,height/2);ctx.moveTo(width/2,0);ctx.lineTo(width/2,height);ctx.stroke();ctx.beginPath();ctx.strokeStyle='#428bca';ctx.lineWidth=2;var first=true;for(var px=0;px=0&&py<=height){if(first){ctx.moveTo(px,py);first=false;}else{ctx.lineTo(px,py);}}}ctx.stroke();var output='Properties:
';if(type==='linear'){output+='Equation: y = '+a+'x + '+c+'
';output+='Slope: '+a+'
';output+='Y-Intercept: (0, '+c+')
';output+='X-Intercept: ('+(-c/a).toFixed(2)+', 0)';}else{var vx=-b/(2*a);var vy=a*Math.pow(vx,2)+b*vx+c;var disc=Math.pow(b,2)-(4*a*c);output+='Equation: y = '+a+'x² + '+(b>=0?'+':")+b+'x + '+(c>=0?'+':")+c+'
';output+='Vertex: ('+vx.toFixed(2)+', '+vy.toFixed(2)+')
';output+='Y-Intercept: (0, '+c+')
';if(disc>0){var x1=(-b+Math.sqrt(disc))/(2*a);var x2=(-b-Math.sqrt(disc))/(2*a);output+='X-Intercepts: ('+x1.toFixed(2)+', 0) and ('+x2.toFixed(2)+', 0)
';}else if(disc===0){output+='X-Intercept: ('+(-b/(2*a)).toFixed(2)+', 0)
';}else{output+='X-Intercepts: None (Complex roots)
';}output+='Discriminant (Δ): '+disc.toFixed(2);}resDiv.innerHTML=output;}window.onload=calculateGraph;

Using the Graphing Calculator

This graphing calculator is designed to help students, teachers, and professionals visualize linear and quadratic functions instantly. Unlike complex handheld devices, this tool focuses on providing key coordinate points—like the vertex, intercepts, and slope—while rendering a visual representation of the curve or line.

To use the calculator, simply select the type of function you wish to analyze. For parabolas, enter the coefficients for the standard form (ax² + bx + c). For straight lines, enter the slope and y-intercept (mx + b).

Coefficient A / Slope (m)
In a quadratic, 'a' determines the width and direction of the parabola. In a linear equation, 'm' represents the steepness or slope.
Coefficient B
The linear term coefficient in a quadratic equation that affects the horizontal shift and the vertex position.
Constant C / Y-Intercept (b)
This value indicates where the graph crosses the Y-axis (the vertical axis).

How It Works

When you input data into the graphing calculator, it performs several algebraic operations simultaneously. For quadratic functions, it utilizes the vertex formula and the discriminant to find the most important points on the plane.

Vertex X-Coordinate = -b / 2a

  • Discriminant (Δ): Calculated as b² – 4ac. This determines how many times the graph touches the X-axis.
  • Vertex: The highest or lowest point of the parabola (the turning point).
  • Roots: Also known as zeros or X-intercepts, found using the Quadratic Formula.
  • Scaling: The calculator automatically scales the visual plot to fit within the viewing window for better visibility.

Calculation Example

Example: Graphing the quadratic function y = x² – 2x – 3.

Step-by-step solution:

  1. Identify Coefficients: a = 1, b = -2, c = -3.
  2. Find Vertex X: x = -(-2) / (2 * 1) = 1.
  3. Find Vertex Y: y = (1)² – 2(1) – 3 = 1 – 2 – 3 = -4. Vertex is (1, -4).
  4. Calculate Discriminant: Δ = (-2)² – 4(1)(-3) = 4 + 12 = 16.
  5. Find X-Intercepts: x = (2 ± √16) / 2 = (2 ± 4) / 2. Roots are 3 and -1.
  6. Result: The graph is a "U-shaped" parabola opening upward, crossing the X-axis at -1 and 3, with its lowest point at (1, -4).

Common Questions

What is a graphing calculator used for?

A graphing calculator is essential for visualizing mathematical relationships. It helps in solving equations, analyzing the behavior of functions (like limits and continuity), and finding key features of graphs that are difficult to calculate manually, such as local minima, maxima, and intersections.

How do I find the roots of a function?

Roots are the X-values where the function equals zero (y=0). In this calculator, for a quadratic equation, we use the quadratic formula. If the discriminant is negative, the function has no real roots, meaning it never crosses the X-axis.

Why is the vertex important?

The vertex represents the absolute maximum or minimum value of a quadratic function. In real-world applications, such as physics or economics, the vertex can represent the peak height of a projectile or the point of minimum cost/maximum profit.

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