Lab 3: Graphing Calculator: Calculating Points on a Graph

New Concept

A graphing calculator can be used to calculate $y$-values and zeros of equations.

What’s next

Next, you’ll learn the keystrokes to find key points on a graph, including zeros, minimums, maximums, and intersections.

To find a y-value for a given x, use the CALC menu's '1: value' feature. To find the x-intercept or 'zero' of an equation, use the '2: zero' feature by setting left and right bounds around the intercept.

Find the y-value of $y = 3x + 6$ for $x = 2.5$. Using '1: value' gives $y = 13.5$. Find the zero of $y = 4x - 12$. Using '2: zero' shows the root is at $x = 3$.

Your graphing calculator is a math whiz! Instead of manually plugging in x-values, use the 1: value function for instant answers. To find where your line crosses the x-axis (the 'zero'), use the 2: zero feature. It's like a treasure hunt on your graph, guiding you to the exact spot where y equals zero.

For parabolas, find the lowest point using '3: minimum' or the highest point using '4: maximum' from the CALC menu. You must set left and right bounds to isolate the vertex of the parabola for the calculation to work.

Find the minimum of $y = x^2 - 2x - 3$. Using '3: minimum' gives the point $(1, -4)$. Find the maximum of $y = -x^2 + 6x - 5$. Using '4: maximum' gives the point $(3, 4)$.

For any U-shaped parabola, your calculator can instantly find its lowest point (minimum) or highest point (maximum). Forget trying to guess! Just use the 3: minimum or 4: maximum functions in the CALC menu. You'll bracket the point, and the calculator will pinpoint the exact vertex, which is the ultimate low or high point.

To find where two lines intersect, graph both equations and use the '5: intersect' function from the CALC menu. Select the first curve, then the second curve, and make a guess near the intersection point to find the solution.

Find the intersection of $y = 2x + 1$ and $y = -x + 10$. Using '5: intersect' reveals the solution is at $(3, 7)$. Find the intersection of $y = 0.5x - 2$ and $y = -1.5x + 6$. The intersection is at $(4, 0)$.

When two lines cross, they share a single, special point. Your calculator's 5: intersect tool is a master detective for finding it. Simply graph both lines, select the intersect tool, and confirm which two lines you're investigating. The calculator will then reveal the exact $(x, y)$ coordinates where your two graphs meet each other.