Graphing Calculator Online

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Graphing Calculator Online
Quadratic: ax² + bx + cLinear: mx + b
Analysis Result:
Enter coefficients and click Analyze.
function updateLabels(){var type=document.getElementById('calc_type').value;if(type==='linear'){document.getElementById('lbl1′).innerHTML='Slope (m):';document.getElementById('lbl2′).innerHTML='Y-Intercept (b):';document.getElementById('row3′).style.display='none';}else{document.getElementById('lbl1′).innerHTML='Coefficient a:';document.getElementById('lbl2′).innerHTML='Coefficient b:';document.getElementById('lbl3′).innerHTML='Constant c:';document.getElementById('row3′).style.display='table-row';}}function calculateGraph(){var type=document.getElementById('calc_type').value;var a=parseFloat(document.getElementById('input1').value);var b=parseFloat(document.getElementById('input2').value);var c=parseFloat(document.getElementById('input3').value)||0;var ans=document.getElementById('answer');var tableDiv=document.getElementById('coordTable');if(isNaN(a)||isNaN(b)){alert('Please enter valid numeric coefficients.');return;}var resultHTML=";var points=[];if(type==='quadratic'){if(a===0){resultHTML='Error: "a" cannot be 0 for a quadratic function.';}else{var disc=(b*b)-(4*a*c);var vertexX=-b/(2*a);var vertexY=(a*vertexX*vertexX)+(b*vertexX)+c;resultHTML='Function: f(x) = '+a+'x² + '+(b >= 0 ? '+'+b : b)+'x + '+(c >= 0 ? '+'+c : c)+'
';resultHTML+='Vertex: ('+vertexX.toFixed(2)+', '+vertexY.toFixed(2)+')
';resultHTML+='Y-Intercept: (0, '+c+')
';if(disc>0){var x1=(-b+Math.sqrt(disc))/(2*a);var x2=(-b-Math.sqrt(disc))/(2*a);resultHTML+='X-Intercepts (Roots): x = '+x1.toFixed(2)+', x = '+x2.toFixed(2)+'
';}else if(disc===0){resultHTML+='X-Intercept (Root): x = '+(-b/(2*a)).toFixed(2)+'
';}else{resultHTML+='X-Intercepts: No real roots (complex).
';}for(var x=-5;x<=5;x++){points.push({x:x,y:(a*x*x)+(b*x)+c});}}}else{resultHTML='Function: f(x) = '+a+'x + '+(b >= 0 ? '+'+b : b)+'
';resultHTML+='Slope: '+a+'
';resultHTML+='Y-Intercept: (0, '+b+')
';resultHTML+='X-Intercept: ('+(-b/a).toFixed(2)+', 0)
';for(var x=-5;x<=5;x++){points.push({x:x,y:(a*x)+b});}}ans.innerHTML=resultHTML;if(document.getElementById('show_table').checked){var t='';for(var i=0;i<points.length;i++){t+='';}t+='
xf(x)
'+points[i].x+''+points[i].y.toFixed(2)+'
';tableDiv.innerHTML=t;}else{tableDiv.innerHTML=";}drawCanvas(points);}function drawCanvas(points){var canvas=document.getElementById('graphCanvas');var ctx=canvas.getContext('2d');var container=document.getElementById('graphCanvasContainer');container.style.display='block';ctx.clearRect(0,0,canvas.width,canvas.height);var margin=30;var width=canvas.width-2*margin;var height=canvas.height-2*margin;var minX=-5;var maxX=5;var minY=Infinity;var maxY=-Infinity;for(var i=0;i<points.length;i++){if(points[i].ymaxY)maxY=points[i].y;}if(maxY===minY){maxY+=1;minY-=1;}ctx.strokeStyle='#ccc';ctx.beginPath();var zeroX=margin+(0-minX)/(maxX-minX)*width;var zeroY=margin+height-(0-minY)/(maxY-minY)*height;ctx.moveTo(margin,zeroY);ctx.lineTo(margin+width,zeroY);ctx.moveTo(zeroX,margin);ctx.lineTo(zeroX,margin+height);ctx.stroke();ctx.strokeStyle='#428bca';ctx.lineWidth=2;ctx.beginPath();for(var i=0;i<points.length;i++){var px=margin+(points[i].x-minX)/(maxX-minX)*width;var py=margin+height-(points[i].y-minY)/(maxY-minY)*height;if(i===0)ctx.moveTo(px,py);else ctx.lineTo(px,py);}ctx.stroke();}

How to Use the Graphing Calculator Online

Our graphing calculator online is designed to help students, educators, and engineers visualize mathematical functions and solve algebraic equations quickly. Whether you are dealing with basic linear equations or complex parabolas, this tool provides the analytical data and visual plotting required for deep understanding.

Select Function Type
Choose between a Quadratic function (ax² + bx + c) or a Linear function (mx + b).
Enter Coefficients
Input the numerical values for 'a', 'b', and 'c'. These determine the shape, position, and orientation of the graph.
Coordinate Table
Toggle this option to see a detailed breakdown of (x, y) coordinates from -5 to 5, perfect for manual sketching or verification.

How It Works: The Math Behind the Graph

When you enter data into the graphing calculator online, it performs several algebraic operations simultaneously to define the properties of your function.

The Quadratic Formula

To find the roots (where the graph crosses the x-axis), the calculator uses the standard quadratic formula:

x = [-b ± sqrt(b² – 4ac)] / 2a

  • Discriminant (b² – 4ac): Determines if there are two real roots, one root, or none.
  • Vertex Calculation: The turning point of the parabola is found using x = -b/2a.
  • Slope (m): For linear equations, this represents the rate of change or "steepness."

Calculation Example

Scenario: You need to graph the function f(x) = x² – 5x + 6 and find its key points.

Step-by-step solution:

  1. Identify Coefficients: a = 1, b = -5, c = 6.
  2. Find Vertex: x = -(-5) / (2 * 1) = 2.5. Calculate y: (2.5)² – 5(2.5) + 6 = -0.25. Vertex = (2.5, -0.25).
  3. Calculate Discriminant: (-5)² – 4(1)(6) = 25 – 24 = 1. Since it's positive, there are two real roots.
  4. Solve for Roots: x = (5 ± sqrt(1)) / 2. Roots are x = 3 and x = 2.
  5. Y-Intercept: Set x to 0. f(0) = 6. Point = (0, 6).

Common Questions

Why is the graphing calculator online showing "No real roots"?

If the discriminant (b² – 4ac) is negative, the parabola does not cross the x-axis. This means the solution involves imaginary numbers, and the graph "floats" above or sits below the x-axis.

Can I use this for homework verification?

Absolutely! This tool is an excellent way to check your manual calculations for vertices, intercepts, and slope. By comparing your hand-drawn graph to the generated coordinate table, you can identify errors in your work instantly.

What does the "a" coefficient do?

In a quadratic function, "a" determines the width and direction of the parabola. If "a" is positive, the graph opens upward (like a smile). If "a" is negative, it opens downward (like a frown). A larger absolute value of "a" makes the graph narrower.

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