Each function including square, can be constructed on graphics. For creation of this graphic representation roots of this quadratic equation pay off.
It is required to you
- - ruler;
- - simple pencil;
- - notebook;
- - handle;
- - template.
Instruction
1. Find roots of a quadratic equation. The quadratic equation with one unknown looks as follows: ax2+bx+c=0. Here x represents required unknown; a, b and c are the known coefficients, at this a 0 should not be equal. If to divide both parts of the set quadratic equation into a coefficient, then receive the given quadratic equation of a type of x2+px+q=0 in which p=b/a and q=c/a. Provided that one of coefficients of b or c, or both are equal to zero, the quadratic equation received by you is called incomplete.
2. Find a discriminant which is calculated by a formula: b2-4ac. In case the value D a more than 0th, quadratic equation has two valid roots; if D=0, the found valid roots are equal among themselves; if D
3. The parabola will be the graphic representation of square function. Define additional data for creation of the schedule of this square function: direction of "branches" of a parabola, its top and also symmetry axis equation. If a> 0, "branches" of a parabola are directed up (otherwise, "branches" will be directed down).
4. For determination of coordinates of top of a parabola find also on a formula: - b/2a then substitute value of "X" in a quadratic equation for obtaining value at.
5. And at last, the equation of an axis of symmetry depends on value of coefficient with in an initial quadratic equation. For example, if the set quadratic equation at = h2-6kh +3, then passes an axis of symmetry across the line in which x =3.
6. Knowing the direction of "branches" of a parabola, coordinate of its top and also a symmetry axis, construct the schedule of the set quadratic equation by means of a template. Designate equation roots on the represented schedule: they will be zero function.