%5E2-in-standard-form.jpeg "(x-4)^2 In Standard Form")
Expanding and Simplifying (x-4)^2 to Standard Form
In mathematics, the standard form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To express (x-4)^2 in standard form, we need to expand the expression and combine like terms.
Expanding the Expression
We can use the FOIL method (First, Outer, Inner, Last) to expand (x-4)^2:
- First: x * x = x^2
- Outer: x * -4 = -4x
- Inner: -4 * x = -4x
- Last: -4 * -4 = 16
Combining these terms, we get:
(x-4)^2 = x^2 - 4x - 4x + 16
Simplifying the Expression
Now, we combine the like terms:
(x-4)^2 = x^2 - 8x + 16
Therefore, the standard form of (x-4)^2 is x^2 - 8x + 16.
Understanding the Result
This equation represents a parabola that opens upwards, with its vertex at the point (4, 0). The standard form helps us easily identify the coefficient of the squared term (a = 1), the coefficient of the linear term (b = -8), and the constant term (c = 16). These values are crucial for analyzing the properties of the parabola and solving related equations.