1.5: Calculator Use with Algebra Expressions
What if you wanted to evaluate the expression \begin{align*}\frac{x^2+4x+3}{2x^2-9x-5}\end{align*} when \begin{align*}x=7\end{align*} ? If you had your calculator handy, it could make things easier, but how would you enter an expression like this into your calculator? Also, how would you tell your calculator that \begin{align*}x=7\end{align*} ? In this Concept, you will learn how to make use of your calculator when evaluating expressions like these.
Guidance
A calculator, especially a graphing calculator, is a very useful tool in evaluating algebraic expressions. A graphing calculator follows the order of operations, PEMDAS. In this section, we will explain two ways of evaluating expressions with a graphing calculator.
Example A
Method #1 This method is the direct input method. After substituting all values for the variables, you type in the expression, symbol for symbol, into your calculator.
Evaluate \begin{align*}[3(x^2 - 1)^2 - x^4 + 12] + 5x^3 - 1\end{align*} when \begin{align*}x = -3\end{align*} .
Substitute the value \begin{align*}x = -3\end{align*} into the expression.
\begin{align*}[3((-3)^2 -1)^2 - (-3)^4 + 12] + 5(-3)^3 - 1\end{align*}
The potential error here is that you may forget a sign or a set of parentheses, especially if the expression is long or complicated. Make sure you check your input before writing your answer. An alternative is to type in the expression in appropriate chunks – do one set of parentheses, then another, and so on.
Example B
Method #2 This method uses the STORE function of the Texas Instrument graphing calculators, such as the TI-83, TI-84, or TI-84 Plus.
First, store the value \begin{align*}x = -3\end{align*} in the calculator. Type -3 [STO] \begin{align*}x\end{align*} . ( The letter \begin{align*}x\end{align*} can be entered using the \begin{align*}x\end{align*} - [VAR] button or [ALPHA] + [STO] ). Then type in the expression in the calculator and press [ENTER] .
The answer is \begin{align*}-13.\end{align*}
Note: On graphing calculators there is a difference between the minus sign and the negative sign. When we stored the value negative three, we needed to use the negative sign, which is to the left of the [ENTER] button on the calculator. On the other hand, to perform the subtraction operation in the expression we used the minus sign. The minus sign is right above the plus sign on the right.
Example C
You can also use a graphing calculator to evaluate expressions with more than one variable.
Evaluate the expression: \begin{align*}\frac{3x^2 - 4y^2 + x^4}{(x + y)^{\frac{1}{2}}}\end{align*} for \begin{align*}x = -2, y = 1\end{align*} .
Store the values of \begin{align*}x\end{align*} and \begin{align*}y\end{align*} : \begin{align*}-2\end{align*} [STO] \begin{align*}x\end{align*} , 1 [STO] \begin{align*}y\end{align*} . The letters \begin{align*}x\end{align*} and \begin{align*}y\end{align*} can be entered using [ALPHA] + [KEY] . Input the expression in the calculator. When an expression shows the division of two expressions, be sure to use parentheses: (numerator) \begin{align*}\div\end{align*} (denominator). Press [ENTER] to obtain the answer \begin{align*}-.8\bar{8}\end{align*} or \begin{align*}-\frac{8}{9}\end{align*} .
Vocabulary
Evaluate: To evaluate means to follow the verbs in the math sentence. Evaluate can also be called simplify or answer.
Guided Practice
Evaluate the expression \begin{align*}\frac{x-y}{x^2 + y^2}\end{align*} for \begin{align*}x = 3, y = -1\end{align*} .
Store the values of \begin{align*}x\end{align*} and \begin{align*}y\end{align*} : \begin{align*}3\end{align*} [STO] \begin{align*}x\end{align*} , -1 [STO] \begin{align*}y\end{align*} . The letters \begin{align*}x\end{align*} and \begin{align*}y\end{align*} can be entered using [ALPHA] + [KEY] . Input the expression in the calculator. When an expression shows the division of two expressions, be sure to use parentheses: (numerator) \begin{align*}\div\end{align*} (denominator). Press [ENTER] to obtain the answer \begin{align*}0.4\end{align*} .
Practice
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Order of Operations (14:23)
In 1-5, evaluate each expression using a graphing calculator.
- \begin{align*}x^2 + 2x - xy\end{align*} when \begin{align*}x = 250\end{align*} and \begin{align*}y = -120\end{align*}
- \begin{align*}(xy - y^4)^2\end{align*} when \begin{align*}x = 0.02\end{align*} and \begin{align*}y = -0.025\end{align*}
- \begin{align*}\frac{x + y - z}{xy + yz + xz}\end{align*} when \begin{align*}x = \frac{1}{2}, \ y = \frac{3}{2}\end{align*} , and \begin{align*}z = -1\end{align*}
- \begin{align*}\frac{(x + y)^2}{4x^2 - y^2}\end{align*} when \begin{align*}x = 3\end{align*} and \begin{align*}y = -5d\end{align*}
- The formula to find the volume of a spherical object (like a ball) is \begin{align*}V = \frac{4}{3}(\pi)r^3\end{align*} , where \begin{align*}r =\end{align*} the radius of the sphere. Determine the volume for a grapefruit with a radius of 9 cm.
In 6-9, insert parentheses in each expression to make a true equation.
- \begin{align*}5 - 2 \cdot 6 - 4 + 2 = 5\end{align*}
- \begin{align*}12 \div 4 + 10 - 3 \cdot 3 + 7 = 11\end{align*}
- \begin{align*}22 - 32 - 5 \cdot 3 - 6 = 30\end{align*}
- \begin{align*}12 - 8 - 4 \cdot 5 = -8\end{align*}
Mixed Review
- Let \begin{align*}x = -1\end{align*} . Find the value of \begin{align*}-9x + 2\end{align*} .
- The area of a trapezoid is given by the equation \begin{align*}A = \frac{h}{2}(a + b)\end{align*} . Find the area of a trapezoid with bases \begin{align*}a = 10 \ cm, b = 15 \ cm\end{align*} , and height \begin{align*}h = 8 \ cm\end{align*} .
- The area of a circle is given by the formula \begin{align*}A = \pi r^2\end{align*} . Find the area of a circle with radius \begin{align*}r = 17\end{align*} inches.
Image Attributions
Here you'll learn how to type an expression into your calculator and evaluate it, either by entering the value(s) of the variable(s) directly into the expression, or by storing the value(s) of the variable(s) in your calculator's memory and then entering the expression.