Substitution

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.

Image of graphing calculator Graphs of two parabolas.  The first is modeled when b=1 and the second is modeled when b = -1.

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

Graphs of two parabolas and their vertices.  The first is modeled when b=1 and the second is modeled when b = -1

 

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.

The first expression line shows the value of m divided by n plus m when m equals 10 and n equals 2.  The second shows the value of a divided by 10 when a equals 2 times b and b is defined in a third line as equal to -5.