symmetrical
7. A parabola is symmetrical about its longitudinal axis, also called longitudinal axis symmetry. This means that the mirror point of the point on the parabola about the longitudinal axis is also on the parabola. If you take any point on the parabola, then at the same height, the point that is axially symmetric about this point is also on the parabola. This symmetry makes the parabola similar in shape on the left and right sides.
2. Definition domain
Domain refers to the range of values of independent variables that can be accepted by a function. For parabola, the domain refers to the set of all real values that the independent variable can take. Is the whole set of real numbers, that is, the interval from negative infinity to positive infinity. This means that any real value on the parabola can be used as an independent variable, and the function will give the value of the corresponding dependent variable.
3. Parity
Parity refers to whether the parabolic function remains unchanged after variable replacement. If the function value of a parabolic function remains unchanged after the independent variable is replaced by -x, then this parabolic function is an even function; If the function value changes after replacement, then the parabolic function is odd function.
4. Zero point
Refers to the point where a parabola intersects the X axis, also known as the root or solution. More precisely, the zero point of the parabola is the x value that makes the parabolic function value zero. This is a problem of the solution of quadratic equation. A parabola can have zero, one or two real number solutions. It depends on the value of the discriminant.
5. Maximum point
The maximum point refers to the vertex of a parabola, which can also be called the extreme point or the maximum point. The function value of parabola takes the maximum or minimum value, depending on the opening direction of parabola. If a is greater than zero, that is, a parabola with an upward opening, the vertex is the minimum point of the parabola. If a is less than zero, that is, a parabola with a downward opening, the vertex is the maximum point of the parabola.
6. Convergence; gather
Convergence means that when the independent variable approaches infinity, the parabolic function value approaches a certain value. When the independent variable x approaches positive infinity or negative infinity, if the parabolic function y = ax? The function value of +bx+c gradually approaches a finite value, so we say it converges to infinity.
7. Focus
Focus refers to the point equidistant from the parabola directrix, which is an important characteristic point of parabola. For a parabola, it has a focus and a directrix. The position of the focal point can be determined by the parametric equation of parabola or focal length.
8. Tangent property
The tangent property means that every point on a parabola has a unique straight line tangent to the tangent of that point. For a parabola, starting from any point on the parabola, a straight line can be found to pass through that point, and this straight line intersects the parabola at that point, that is, this straight line is tangent to the tangent of the parabola.
9. The relationship between independent variables
The relationship between independent variables refers to the relationship between independent variables and dependent variables in parabolic function expressions. The relationship between the independent variables of parabola function is the basis of parabola definition. By studying the relationship between independent variables, we can deeply understand and analyze the characteristics and properties of parabola and its relationship with other mathematical concepts.
10. Physical application
It refers to the application of the properties and characteristics of parabola to practical problems and phenomena in physics. Parabola is a conic curve, which is widely used in engineering and physics.
Some applications of parabola in physics make full use of the geometric characteristics and motion laws of parabola, which plays an important role in solving practical problems and designing new technologies.