100 x Square - 20 x + 1: Understanding the Quadratic Expression
In this article, we will delve into the world of quadratic expressions, specifically exploring the equation 100 x square - 20 x + 1. We will break down the components of this equation, understand its structure, and examine its properties.
What is a Quadratic Expression?
A quadratic expression is a polynomial expression of degree two, which means the highest power of the variable (in this case, x) is two. The general form of a quadratic expression is:
ax^2 + bx + c
where a, b, and c are constants, and x is the variable.
Components of 100 x Square - 20 x + 1
Let's dissect the given equation:
100 x square - 20 x + 1
- 100 x square: This term represents the squared variable x, multiplied by the coefficient 100.
- -20 x: This term represents the variable x, multiplied by the coefficient -20.
- + 1: This is a constant term, which does not involve the variable x.
Graphical Representation
The graph of a quadratic expression is a parabola that opens upward or downward. The shape and position of the parabola depend on the coefficients a, b, and c.
In this case, since a = 100 is a positive number, the parabola opens upward. The vertex of the parabola can be found by using the formula:
x = -b / 2a
Substituting the values, we get:
x = -(-20) / (2 * 100) = 1/10
The y-coordinate of the vertex can be found by plugging in the x-coordinate into the equation:
y = 100 * (1/10)^2 - 20 * (1/10) + 1 = 1/4 - 2 + 1 = -1/4
So, the vertex of the parabola is at the point (1/10, -1/4).
Properties of 100 x Square - 20 x + 1
Some important properties of this quadratic expression include:
- Axis of Symmetry: The axis of symmetry is the vertical line that passes through the vertex of the parabola. In this case, the axis of symmetry is x = 1/10.
- x-Intercepts: The x-intercepts are the points where the parabola intersects the x-axis. To find the x-intercepts, we set y = 0 and solve for x. In this case, the x-intercepts are x = -1/10 and x = 1.
- y-Intercept: The y-intercept is the point where the parabola intersects the y-axis. In this case, the y-intercept is y = 1.
Conclusion
In this article, we have explored the quadratic expression 100 x square - 20 x + 1, breaking down its components, understanding its structure, and examining its properties. We have also discussed the graphical representation of the equation and its important properties, such as the axis of symmetry, x-intercepts, and y-intercept. By understanding quadratic expressions like this one, we can better analyze and solve problems in mathematics and real-world applications.
