Square Root Curve Calculator
Convert a percentage grade into a square root curve grade using SRG = sqrt(grade) × 10, with instant calculation preview.
Equation Preview
Helping Notes
Square root curve grading boosts lower percentages using SRG = √G × 10; input is the original percentage only.
Keep G between 0 and 100 for typical grading scales; the result is shown instantly with the formula substitution.
Results
Inputs Summary
Square Root Curve Grade
Computation Details
What Is a Square Root Curve Calculator?
The Square Root Curve Calculator analyzes functions of the form . These curves arise from the parent function through translations, scalings, and reflections. Because the square‑root requires a nonnegative radicand, domains and ranges depend on parameters and orientation. This tool automatically determines the real domain, plots the curve, computes tangents/slopes, and reports intercepts, key points, and inverse relations. It also rewrites expressions into equivalent forms (e.g., factoring out under‑root constants) to make transformations and rates of change immediately visible for algebra and precalculus practice.
About the Square Root Curve Calculator
Given parameters with , the domain is defined by the radicand constraint (so when , and when ). The range follows from the vertical transform: if then ; if then . Derivatives use the chain rule with so that on the interior of the domain. Intercepts, if any, are solved by setting or with the domain restriction applied. The inverse relation (when monotone on its domain) is , reflecting across . Throughout, the calculator renders responsive formulas and exact/decimal values so you can verify algebraic steps on any screen size.
Model:
Domain:
Range (real):
Derivative:
Inverse (monotone):
Scaling under the root:
How to Use This Square Root Curve Calculator
- Enter parameters or an explicit function like .
- Specify the x‑interval; the tool enforces the domain automatically.
- Compute to view the plot, derivative, tangent at a chosen point, intercepts (if real), and inverse relation.
- Copy the stepwise formulas and numeric evaluations for assignments or reports.
Examples
- Parent curve: , domain . At , slope and point .
- Shifted & stretched: . Domain , range , no real x‑intercept.
- Under‑root scaling: (horizontal compression by factor 1/4 becomes vertical stretch by 2).
- Reflection: flips across the line ; range .
- Inverse relation: For , inverse is with .
Formula Snippets Ready for Rendering
FAQs
Why does the domain start at h?
Because the radicand must be nonnegative: , which yields for and for .
How do parameter values affect the graph?
shifts horizontally, vertically, scales/reflects vertically, and compresses/reflects horizontally under the square root.
Can the curve have an x‑intercept?
Yes, if solving yields an in the domain. Some transformations produce no real intercepts.
Where is the derivative undefined?
At the endpoint where the radicand is zero (e.g., for ) the slope tends to infinity; differentiate only on the interior.
How do I find the inverse function?
Isolate the root: subtract , divide by , square both sides, and solve for to get .
What happens if b is negative?
The domain flips to and the graph opens to the left. The calculus formulas still apply on that domain.
Can I use this for data modeling?
Yes. Square‑root models describe diminishing returns and diffusion‑like growth; fit from data, then analyze with this calculator.