2%2B8%3D0-values-of-a-b-and-c.jpeg "(x-4)2+8=0 Values Of A B And C")
Identifying the Values of a, b, and c in a Quadratic Equation
The equation (x - 4)² + 8 = 0 represents a quadratic equation in standard form. Understanding the values of a, b, and c is crucial for solving quadratic equations using various methods like the quadratic formula.
Expanding the Equation
Before we can determine the values, let's expand the equation to get it in the standard form ax² + bx + c = 0.
- Expand the square: (x - 4)² = (x - 4)(x - 4) = x² - 8x + 16
- Substitute back into the equation: x² - 8x + 16 + 8 = 0
- Simplify: x² - 8x + 24 = 0
Determining a, b, and c
Now that the equation is in standard form, we can easily identify the coefficients:
- a = 1: The coefficient of the x² term.
- b = -8: The coefficient of the x term.
- c = 24: The constant term.
Importance of a, b, and c
The values of a, b, and c are essential for:
- Solving the quadratic equation: Using the quadratic formula, we can find the roots (solutions) of the equation.
- Analyzing the graph of the quadratic function: The values of a, b, and c influence the shape, position, and direction of the parabola representing the function.
- Understanding the nature of the roots: Whether the roots are real or complex, distinct or repeated, can be determined using the discriminant (b² - 4ac).
By understanding the significance of these coefficients, you gain a deeper understanding of quadratic equations and their applications.