Quadratic Equation: 4x2 - 16 = 0
In this article, we will explore the quadratic equation 4x2 - 16 = 0, its properties, and how to solve it.
What is a Quadratic Equation?
A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable (x) is two. The general form of a quadratic equation is:
ax2 + bx + c = 0
where a, b, and c are constants, and x is the variable.
The Equation: 4x2 - 16 = 0
The equation 4x2 - 16 = 0 is a quadratic equation in which:
- a = 4
- b = 0
- c = -16
Properties of the Equation
The equation 4x2 - 16 = 0 has some interesting properties:
- Parabola: The graph of the equation is a parabola that opens upward.
- X-intercepts: The equation has two x-intercepts, which are the solutions to the equation.
- Axis of Symmetry: The axis of symmetry is the vertical line that passes through the vertex of the parabola.
Solving the Equation
To solve the equation 4x2 - 16 = 0, we can start by factoring the left-hand side of the equation:
4x2 - 16 = (2x + 4)(2x - 4) = 0
This tells us that either (2x + 4) = 0 or (2x - 4) = 0.
Solving for the first factor, we get:
2x + 4 = 0 --> 2x = -4 --> x = -2
And solving for the second factor, we get:
2x - 4 = 0 --> 2x = 4 --> x = 2
Therefore, the solutions to the equation 4x2 - 16 = 0 are x = -2 and x = 2.
Conclusion
In this article, we explored the quadratic equation 4x2 - 16 = 0, its properties, and how to solve it. We learned that the equation has two solutions, x = -2 and x = 2, and that the graph of the equation is a parabola that opens upward.
