# #36. Find the Difference Quotient (f(x + h) - f(x))/h for the Function f(x) = 2x^2 - 5x | Summary and Q&A

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June 22, 2018
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The Math Sorcerer
#36. Find the Difference Quotient (f(x + h) - f(x))/h for the Function f(x) = 2x^2 - 5x

## TL;DR

Learn how to find the difference quotient for a quadratic function by evaluating f(X+h) and simplifying the expression.

## Key Insights

• ☠️ The difference quotient is used to find the average rate of change of a function over a small interval.
• ❓ Substituting (X+h) for X in a function is a common technique in calculus and algebra.
• 😑 Simplifying the expression involves expanding and combining like terms.

## Transcript

let's workout problem number 36 find the difference quotient for the function below simplify your answer as much as possible so the function given is f of X equals 2x squared minus 5x and we have to find the difference quotient for this function so the difference quotient is f of X plus h minus f of X and it's all over H ok it's the first thing we ... Read More

### Q: What is the first step to finding the difference quotient for a quadratic function?

The first step is to evaluate f(X+h) by replacing all instances of X in the function with (X+h).

### Q: Why is it important to use parentheses when substituting (X+h) into the quadratic function?

It is important to use parentheses to properly distribute and simplify the expression, ensuring accurate results.

### Q: How do you simplify the expression after evaluating f(X+h) and f(X)?

After evaluating, you expand and simplify the terms, combining like terms and distributing any coefficients.

### Q: What is the final answer for the difference quotient of the given quadratic function?

The final answer is 4x + 2h - 5, which is obtained after simplifying the expression and canceling out the duplicate terms.

## Summary & Key Takeaways

• The content teaches how to find the difference quotient for a given quadratic function.

• It involves substituting (X+h) for X in the function, simplifying the expression, and dividing it by h.

• The final answer is 4x + 2h - 5.