Graph Function Calculator

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Quadratic Function Evaluator

Enter values and click "Calculate Y-Value"
function calculateQuadratic() { var a = parseFloat(document.getElementById('coeffA').value); var b = parseFloat(document.getElementById('coeffB').value); var c = parseFloat(document.getElementById('coeffC').value); var x = parseFloat(document.getElementById('xValue').value); if (isNaN(a) || isNaN(b) || isNaN(c) || isNaN(x)) { document.getElementById('result').innerHTML = 'Please enter valid numbers for all fields.'; return; } var y = (a * x * x) + (b * x) + c; document.getElementById('result').innerHTML = 'For y = ' + a + 'x² + ' + b + 'x + ' + c + ' and x = ' + x + ', the Y-Value is: ' + y.toFixed(4) + ''; }

Understanding the Quadratic Function Evaluator

A quadratic function is a polynomial function of the form y = ax² + bx + c, where 'a', 'b', and 'c' are constant coefficients, and 'a' is not equal to zero. The graph of a quadratic function is a U-shaped curve called a parabola. This calculator helps you evaluate the 'y' value for any given 'x' value on a specific quadratic function.

What do the coefficients mean?

  • Coefficient 'a': This determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. A larger absolute value of 'a' makes the parabola narrower.
  • Coefficient 'b': This coefficient, along with 'a', influences the position of the parabola's vertex (the turning point) and its axis of symmetry.
  • Coefficient 'c': This is the constant term and represents the y-intercept of the parabola – the point where the graph crosses the y-axis (when x = 0, y = c).

How to Use This Calculator

Our Quadratic Function Evaluator simplifies the process of finding a 'y' value for any point on your quadratic curve. Follow these simple steps:

  1. Enter Coefficient 'a': Input the numerical value for 'a' from your quadratic equation (e.g., for y = 2x² + 3x - 1, enter 2).
  2. Enter Coefficient 'b': Input the numerical value for 'b' (e.g., for y = 2x² + 3x - 1, enter 3).
  3. Enter Coefficient 'c': Input the numerical value for 'c' (e.g., for y = 2x² + 3x - 1, enter -1).
  4. Enter X-Value: Input the specific 'x' value for which you want to find the corresponding 'y' value.
  5. Click "Calculate Y-Value": The calculator will instantly compute and display the 'y' value based on your inputs.

Example Calculation

Let's say you have the quadratic function: y = 3x² - 5x + 2. You want to find the 'y' value when x = 4.

  • Coefficient 'a' = 3
  • Coefficient 'b' = -5
  • Coefficient 'c' = 2
  • X-Value = 4

Using the formula y = ax² + bx + c:

y = 3 * (4)² + (-5) * (4) + 2

y = 3 * 16 - 20 + 2

y = 48 - 20 + 2

y = 28 + 2

y = 30

The calculator would output: "For y = 3x² + -5x + 2 and x = 4, the Y-Value is: 30.0000".

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