(1) are all expressions: functions, equations, inequalities;

(2) They all contain similar algebraic expressions: ax? +bx+c；

(3) Their algebraic expressions all contain only one unknown (unary);

(4) The highest number of unknowns in its algebraic expression is quadratic.

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Difference:

(1) quadratic function, unary quadratic equation, unary quadratic inequality

The conceptual categories of are function, equation and inequality respectively.

(2) In quadratic function, the algebraic expression ax? +bx+c equals the dependent variable y;

In the unary quadratic equation, the algebraic expression ax? +bx+c equals zero;

In the unary quadratic inequality, the algebraic expression ax? +bx+c is greater than or less than zero;

(3) Image:

The image of quadratic function is a curve: parabola;

The solution of an unary quadratic equation is a point: two points or a point or no point;

The solution set of the unary quadratic inequality is a line segment or a ray.

Contact person:

The knowledge of (1) unary quadratic equation is the basic knowledge of learning quadratic function and unary quadratic inequality.

(2) Let the quadratic function y=ax? Y=0 +bx+c, then the original formula becomes the quadratic equation ax? +bx+c=0，

Let the unary quadratic inequality axe? The equal sign of +bx+c > 0 becomes the equal sign, and the original formula becomes the quadratic equation ax? +bx+c=0 .

(3) Quadratic function y=ax? The abscissas x 1 and X2 (X 1 < X2) of the intersection of +bx+c parabola and x axis are unary quadratic equations ax? Two +bx+c=0.

(The parabola intersects with the X axis, that is, the equation has two identical roots; If there is no intersection, the equation has no solution. )

Unary quadratic inequality ax? The solution set of +bx+c > 0 is: x < x 1 or x > x2.

For the axe? +bx+c < 0, and the solution set is: x 1 < x < x2.