# Difference quotient for $$$f{\left(x \right)} = 5 x^{2} - 3$$$

### Your Input

**Find the difference quotient for $$$f{\left(x \right)} = 5 x^{2} - 3$$$.**

### Solution

The difference quotient is given by $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h}$$$.

To find $$$f{\left(x + h \right)}$$$, plug $$$x + h$$$ instead of $$$x$$$: $$$f{\left(x + h \right)} = 5 \left(x + h\right)^{2} - 3$$$.

Finally, $$$\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h} = \frac{\left(5 \left(x + h\right)^{2} - 3\right) - \left(5 x^{2} - 3\right)}{h} = 5 h + 10 x$$$.

### Answer

**The difference quotient for $$$f{\left(x \right)} = 5 x^{2} - 3$$$A is $$$5 h + 10 x$$$A.**