casio fx 9750g plus calculator Guide
Quadratic Equation Solver (ax² + bx + c = 0)
This tool demonstrates a core function of the casio fx 9750g plus calculator: solving polynomial equations. Enter the coefficients ‘a’, ‘b’, and ‘c’ to find the roots of the quadratic equation.
Equation Roots (x₁, x₂)
Discriminant (Δ)
1.00
Vertex (x, y)
(1.50, -0.25)
Equation Type
Two Real Roots
Parabola Graph
Visual representation of the equation y = ax² + bx + c. The red dots mark the roots.
Table of (x, y) coordinates around the vertex.
| x | y = f(x) |
|---|
What is the casio fx 9750g plus calculator?
The casio fx 9750g plus calculator is a powerful and versatile graphing calculator designed for students and professionals in mathematics, science, and engineering. It features a large, high-resolution dot matrix display that makes it easy to visualize graphs and complex calculations. Unlike basic scientific calculators, the casio fx 9750g plus calculator comes with an icon-based menu, which simplifies navigation and allows users to quickly select from a wide range of functions, including graphing, statistics, and programming. It is an essential tool for high school and college-level coursework, particularly in subjects like algebra, calculus, and physics.
This calculator is primarily for anyone who needs to perform graphical analysis of functions, solve complex equations, or work with statistical data. Its ability to plot graphs of rectangular, polar, and parametric equations makes it invaluable for visual learners. A common misconception is that these devices are only for advanced mathematicians. However, the intuitive interface of the casio fx 9750g plus calculator makes it accessible even for beginners learning algebra. It provides a bridge between abstract formulas and their graphical representations. Another product to consider for more advanced features is the Casio fx-9750GIII.
casio fx 9750g plus calculator Formula and Mathematical Explanation
One of the most-used features of a graphing calculator like the casio fx 9750g plus calculator is its built-in equation solver. For quadratic equations, which take the form ax² + bx + c = 0, the calculator uses the quadratic formula to find the roots (the values of ‘x’ that solve the equation). The formula is:
x = [-b ± √(b² – 4ac)] / 2a
The expression inside the square root, Δ = b² – 4ac, is called the discriminant. Its value determines the nature of the roots:
- If Δ > 0, there are two distinct real roots. The parabola intersects the x-axis at two different points.
- If Δ = 0, there is exactly one real root (a repeated root). The vertex of the parabola touches the x-axis.
- If Δ < 0, there are two complex conjugate roots. The parabola does not intersect the x-axis. The casio fx 9750g plus calculator can handle complex number calculations.
Variables in the Quadratic Formula
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| a | The coefficient of the x² term | Unitless | Any non-zero number |
| b | The coefficient of the x term | Unitless | Any number |
| c | The constant term | Unitless | Any number |
| x | The unknown variable whose value we are solving for | Unitless | Real or Complex Numbers |
Practical Examples (Real-World Use Cases)
The true power of the casio fx 9750g plus calculator shines in its ability to model real-world scenarios. Here are a couple of examples. For more on the basics, you might read about graphing calculator basics.
Example 1: Projectile Motion
An object is thrown upwards from a height of 2 meters with an initial velocity of 15 m/s. The height (h) of the object after ‘t’ seconds can be modeled by the equation: h(t) = -4.9t² + 15t + 2. To find when the object hits the ground, we set h(t) = 0.
- Inputs: a = -4.9, b = 15, c = 2
- On the casio fx 9750g plus calculator: Navigate to the Equation (EQUA) menu, select Polynomial (F2), choose Degree 2, and input the coefficients.
- Output: The calculator provides two roots: t ≈ 3.18 seconds and t ≈ -0.13 seconds. Since time cannot be negative, the object hits the ground after approximately 3.18 seconds.
Example 2: Maximizing Revenue
A company finds that its revenue (R) from selling an item at price ‘p’ is given by the function R(p) = -50p² + 1000p. The company wants to find the price that maximizes revenue. This corresponds to the vertex of the parabola.
- Inputs: a = -50, b = 1000, c = 0
- On the casio fx 9750g plus calculator: You can graph this function in the GRAPH menu. After drawing the graph, use the G-Solve (F5) function and select MAX to find the vertex.
- Output: The calculator will show that the maximum occurs at p = 10. This means a price of $10 will maximize revenue. Our web-based tool above also calculates the vertex for any quadratic equation. A guide on understanding calculus can provide deeper insights into maximization problems.
How to Use This casio fx 9750g plus calculator Solver
This online calculator is designed to mimic the core equation-solving functionality of your casio fx 9750g plus calculator. Follow these steps:
- Enter Coefficients: Input the values for ‘a’, ‘b’, and ‘c’ from your equation into the respective fields. The ‘a’ value cannot be zero.
- View Real-Time Results: As you type, the results will update automatically. The main result, the roots of the equation, are displayed prominently.
- Analyze Intermediate Values: Check the discriminant to understand the nature of the roots (real or complex). The vertex shows the turning point of the parabola (maximum or minimum).
- Interpret the Graph: The chart provides a visual of the parabola. The red dots indicate where the graph crosses the x-axis, which are the real roots of the equation. This is a key feature of any casio vs texas instruments comparison.
- Review the Data Table: The table shows specific (x, y) points on the curve, helping you trace the parabola’s path, a feature also available in the table mode of a casio fx 9750g plus calculator.
Key Factors That Affect Quadratic Equation Results
The output of a quadratic equation is entirely dependent on its coefficients. Understanding how each one affects the result is fundamental for anyone using a casio fx 9750g plus calculator for algebraic analysis.
- The ‘a’ Coefficient (Curvature): This value determines how wide or narrow the parabola is and its direction. If ‘a’ is positive, the parabola opens upwards (a “smile”). If ‘a’ is negative, it opens downwards (a “frown”). A larger absolute value of ‘a’ makes the parabola narrower.
- The ‘b’ Coefficient (Position of Vertex): The ‘b’ coefficient, in conjunction with ‘a’, shifts the position of the axis of symmetry and the vertex. The x-coordinate of the vertex is located at -b/(2a).
- The ‘c’ Coefficient (Y-Intercept): This is the simplest factor. The value of ‘c’ is the y-intercept of the graph—the point where the parabola crosses the vertical y-axis. It shifts the entire graph up or down.
- The Discriminant (b² – 4ac): This single value, derived from all three coefficients, is the most critical factor in determining the nature of the roots. It dictates whether the equation will have two real solutions, one real solution, or two complex solutions. This is a core concept for anyone learning to program on a programming on a calculator.
- Ratio of ‘b’ to ‘a’ and ‘c’: The interplay between the coefficients is complex. For instance, even with a large positive ‘c’ (high y-intercept), a sufficiently large negative ‘b’ can pull the vertex down enough to create real roots. Experimenting with these values on the casio fx 9750g plus calculator is the best way to build intuition.
- The Sign of ‘a’ and ‘c’: If ‘a’ and ‘c’ have opposite signs (one positive, one negative), the discriminant (b² – 4ac) will always be positive, because -4ac will be a positive term. This guarantees there will always be two distinct real roots.
Frequently Asked Questions (FAQ)
1. Can the casio fx 9750g plus calculator solve equations other than quadratics?
Yes. The casio fx 9750g plus calculator can solve polynomial equations up to the 6th degree. It also has solvers for systems of linear equations with up to six unknowns.
2. How do I graph a function on the casio fx 9750g plus calculator?
From the main menu, select the “GRAPH” icon. You will be presented with a list where you can enter one or more functions (e.g., Y1 = X² – 3). Once entered, press the “DRAW” button to see the graph.
3. Does this calculator work for statistics?
Absolutely. The casio fx 9750g plus calculator has a comprehensive “STAT” mode for univariate and bivariate statistical calculations, various regression models, and statistical graphs like histograms and box plots. You can find more info by checking guides on statistics mode on casio.
4. Can I write my own programs on the casio fx 9750g plus calculator?
Yes, it includes a BASIC-like programming function, allowing you to create custom programs to solve repetitive problems or perform complex calculations. This is a powerful feature for advanced users.
5. What is the difference between the fx-9750G PLUS and the newer fx-9750GIII?
The fx-9750GIII is a newer model with several enhancements, including a “Natural Textbook Display” that shows equations and fractions as they appear in textbooks, a faster processor, and Python programming capabilities. However, the core graphing and solving functions of the casio fx 9750g plus calculator remain foundational in the new model.
6. How do I reset my casio fx 9750g plus calculator?
To perform a full reset, you need to access the memory menu. Be careful, as this will erase stored data. It’s often easier to just reset the specific mode you are in or clear the screen entries. Consult the user manual for detailed reset instructions.
7. Can this calculator handle complex numbers?
Yes, the casio fx 9750g plus calculator can perform calculations with complex numbers, including displaying the roots of an equation in a+bi form. You may need to change the mode in the setup menu to enable this.
8. Is the casio fx 9750g plus calculator allowed on standardized tests?
The policies for standardized tests (like the SAT, ACT, AP) change over time and vary by test. While many Casio graphing calculators are permitted, you MUST check the official testing agency’s most current list of approved calculators before your exam. Newer models like the GIII are often explicitly listed.