Our **substitution** feature allows you to answer the question "What *would* be the value of this expression if we substituted a different value for A?," without ever changing the original value of A.

Using the ‘with’ substitution function, you can replace a variable in an expression with a constant value, another variable expression, or a list.

You can find this function in the “Advanced” section of the “Functions” menu on the keypad, or ‘with’ can also be typed directly into an expression line using your keyboard.

### Substitution within a Function

Where would the parabola \(f\left(x\right)=ax^{2}+bx+c\) move if \(b\) were \(-1\)? Model \(f\left(x\right)\) after substituting \(b\) with \(-1\) to visualize the change.

Next, trying graphing the vertex of the original function \((V)\) and using substitution to also graph the vertex when \(b = -1\).

### Substitution with a List

How do changes to \(a\), \(b\), and \(c\) affect the path of the vertex of the parabola? By substituting \(b\) with a list, you can model the path that the vertex would take.

First, graph the vertex of the original function \((V)\). Then, try substituting \(b\) with a list of possible values.

**You try!** Open the graph below and try it out. Use the sliders to change the values of \(a\), \(b\), and \(c\) and see how they compare to the path graphed in line 6. Example Graph.

**Note:** You can learn more about lists in our Help Center.

### Substitution within the Same Expression Line

You can evaluate expressions by substituting variables with constant values in the same line. You can also substitute a variable with another expression, but if that expression depends on a free variable, it will need to be defined separately.

By substituting the variable \(L\) with a list of values, you can quickly plot points along the function \(y=sin(x)\)