Desmos Calculator

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Desmos-Style Function Calculator
Quadratic Function: f(x) = ax² + bx + cLinear Function: f(x) = mx + b
Analysis Results:

Please enter coefficients to see the function analysis.

function updateLabels(){var type=document.getElementById('calc_type').value;var l1=document.getElementById('label1');var l2=document.getElementById('label2');var l3=document.getElementById('label3');var i3=document.getElementById('input3′);if(type==='linear'){l1.innerHTML='Slope (m):';l2.innerHTML='Y-Intercept (b):';l3.style.display='none';i3.style.display='none';}else{l1.innerHTML='Coefficient (a):';l2.innerHTML='Coefficient (b):';l3.style.display='block';i3.style.display='block';}}function resetCalc(){document.getElementById('answer').innerHTML='
Please enter coefficients to see the function analysis.

';updateLabels();}function calculateDesmos(){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);var x=parseFloat(document.getElementById('inputX').value);var showSteps=document.getElementById('showSteps').checked;if(isNaN(a)||isNaN(b)||isNaN(x)){alert('Please enter valid numeric values.');return;}var resultHTML=";if(type==='linear'){var y=a*x+b;var xIntercept=-b/a;resultHTML+='Function: f(x) = '+a+'x + '+b+'
';resultHTML+='Value at f('+x+'): '+y.toFixed(4)+'
';if(showSteps){resultHTML+='X-Intercept: ('+xIntercept.toFixed(4)+', 0)
';resultHTML+='Y-Intercept: (0, '+b+')
';resultHTML+='Slope: '+a;}}else{if(isNaN(c)){alert('Please enter a value for c.');return;}var yQuadratic=(a*Math.pow(x,2))+(b*x)+c;var disc=(b*b)-(4*a*c);var vertexX=-b/(2*a);var vertexY=a*Math.pow(vertexX,2)+(b*vertexX)+c;resultHTML+='Function: f(x) = '+a+'x² + '+b+'x + '+c+'
';resultHTML+='Value at f('+x+'): '+yQuadratic.toFixed(4)+'
';if(showSteps){resultHTML+='Vertex: ('+vertexX.toFixed(4)+', '+vertexY.toFixed(4)+')
';resultHTML+='Discriminant (Δ): '+disc.toFixed(4)+'
';if(disc>0){var r1=(-b+Math.sqrt(disc))/(2*a);var r2=(-b-Math.sqrt(disc))/(2*a);resultHTML+='Roots: x₁='+r1.toFixed(4)+', x₂='+r2.toFixed(4);}else if(disc===0){var r0=-b/(2*a);resultHTML+='Root: x='+r0.toFixed(4);}else{resultHTML+='Roots: No real roots (complex roots exist).';}}}document.getElementById('answer').innerHTML='
'+resultHTML+'
';}

Desmos Calculator Use

This desmos calculator simulator is designed to help students, teachers, and professionals analyze mathematical functions quickly and accurately. Whether you are working with simple linear equations or more complex quadratic functions, this tool provides the essential outputs you would typically look for in a graphing environment, such as y-values, intercepts, and vertices.

By using this interface, you can simulate the evaluation phase of a graphing project. Simply choose your function type, input your coefficients, and the calculator handles the algebraic heavy lifting instantly.

Coefficient (a / m)
The leading coefficient. In linear equations, this is the slope. In quadratic equations, this determines the width and direction of the parabola.
Coefficient (b)
The linear coefficient or y-intercept in linear mode. It affects the position and slope of the curve.
Constant (c)
The vertical shift or y-intercept for quadratic functions.
Evaluate at x
The specific horizontal coordinate where you want to find the corresponding height (y-value) of the function.

How It Works

The math behind this tool mimics the logic used by the desmos calculator engine. It uses standard algebraic formulas to break down functions into their component parts.

Quadratic Formula: x = [-b ± sqrt(b² – 4ac)] / 2a

  • Discriminant (Δ): Calculated as b² – 4ac. This tells us how many real roots exist.
  • Vertex (h, k): Found using h = -b/2a and k = f(h). This is the peak or valley of the graph.
  • Slope-Intercept: For linear modes, we use y = mx + b to find the trajectory of the line.

Calculation Example

Example: Analyze the quadratic function f(x) = 1x² – 4x + 3 and evaluate it at x = 5.

Step-by-step solution:

  1. Identify coefficients: a = 1, b = -4, c = 3.
  2. Evaluate at x = 5: f(5) = 1(5)² – 4(5) + 3 = 25 – 20 + 3 = 8.
  3. Calculate Vertex: x = -(-4) / (2*1) = 2. f(2) = (2)² – 4(2) + 3 = -1. Vertex is (2, -1).
  4. Calculate Roots: Δ = (-4)² – 4(1)(3) = 16 – 12 = 4. Roots = (4 ± 2) / 2. Roots are x=3 and x=1.
  5. Result: Value is 8, Vertex at (2,-1), Roots at 1 and 3.

Common Questions

Why use a desmos calculator for basic functions?

While basic calculators only provide numeric answers, a desmos-style approach allows you to visualize the relationship between variables. Even without a graph, knowing the vertex and intercepts helps you "see" the math.

What is the discriminant in a quadratic equation?

The discriminant (b² – 4ac) determines the nature of the roots. If it is positive, you have two real roots. If zero, one real root. If negative, the graph never touches the x-axis, resulting in complex/imaginary roots.

Can this calculate slope for linear equations?

Yes, in the linear mode, the "m" input represents the slope, which is the "rise over run" or the rate of change for the function.

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