Final answer:
A unique quadratic function in standard form can be created by choosing characteristics and specific values for the coefficients a, b, and c in the standard equation y = ax^2 + bx + c. Using Desmos or a graphing calculator, enter the values and adjust as needed to refine the graph of the function.
Step-by-step explanation:
To write a unique quadratic function equation in standard form using a graphing calculator or a tool like Desmos, you can follow these steps:
- Determine the desired characteristics of the quadratic function such as the direction of the parabola (upward or downward), the vertex location, and whether it has real roots (x-intercepts).
- Decide on specific values for the coefficients in the standard form equation, which is y = ax^2 + bx + c.
- Using a graphing calculator or Desmos, enter your chosen coefficients to graph the quadratic function.
- If needed, adjust the coefficients to ensure the graph matches your desired characteristics.
As an example, if you want a parabola that opens upwards with its vertex at (3, -2) and intercepts the y-axis at 4, you can start with a vertex form of the function y = a(x - h)^2 + k, and insert the vertex values h = 3 and k = -2 to get y = a(x - 3)^2 - 2. Since it intercepts the y-axis at 4, when x = 0, y should be 4. You determine a by solving 4 = a(0 - 3)^2 - 2, which gives a = 1. So the function in vertex form is y = (x - 3)^2 - 2, which can be expanded to the standard form y = x^2 - 6x + 7.