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Root formula method` How can I calculate two after I get Delta? Forget it and you can't find the book`
X = - B - △ is divided by 2
Solving equation (1) 2x + X-6 = 0 (2) x square + 2 times root sign 3x = - 3 (3) 2x square - 7x = - 8
(1) 2X + X-6 = 0 x = [- 1 ± √ (1 2 + 4 × 2 × 6)] / 2 * 2x = (- 1 ± √ 49) / 4x = (- 1 ± 7) / 4 ̺ X1 = - 2x2 = 3 / 2 (2) x square + 2 times root, 3x = - 3 x = [- 2 √ 3 ± √ (2 √ 3) 2 √ 4 * 3] / 2x = (- 2 √ 3 ± 0) / 2x = - 3 (3) 2x square-7x = - 82x ^ ^ 7x + 8 = 000x = 8 = 0 = 0 = 3 (3) 2x square-7x = - 82x-7x + 8 = 0 = 8 = 0 = 8 = 0 = 8 = 0 = 3 (3 x =
rectangle How much does it take to completely enclose a box 2 inches long, 3 inches wide and 4 inches high Square inch wrapping paper?
2 × 3 × 2 + 2 × 4 × 2 + 3 × 4 × 2 = 52,
How to do if C term is 0
If the term C is zero, then C is equal to 0. Just bring it into the root formula directly
Root formula method (factorization)
The formula for finding roots is x = - B, and the discriminant (square of B minus 4ac) divided by 2a is written in the positive and negative root sign
What is the root formula?
The two roots of the quadratic equation AX ^ 2 + BX + C = 0 are
When B ^ 2-4ac > = 0
Is x = [- B ± (b ^ 2-4ac) ^ (1 / 2)] / 2A;
When B ^ 2-4ac
Formula for finding roots of quadratic equation of one variable Can there be?
The formula for finding roots of quadratic equation with one variable is as follows:
When Δ = B ^ 2-4ac ≥ 0, x = [- B ± (b ^ 2-4ac) ^ (1 / 2)] / 2A
When Δ = B ^ 2-4ac < 0, x = {- B ± [(4ac-b ^ 2) ^ (1 / 2)] I} / 2A (I is an imaginary number unit)
The matching method of one variable quadratic equation is as follows
Ax ^ 2 + BX + C = 0 (a, B, C are constants)
x^2+bx/a+c/a=0
(x+b/2a)^2=(b^2-4ac)/4a^2
x+b/2a=±(b^2-4ac)^(1/2)/2a
x=[-b±(b^2-4ac)^(1/2)]/2a
In fact, the matching method is similar to the formula method, but more intuitive
Formula for finding roots of quadratic function of one variable
x=[-b±√(b^2-4ac)]/(2a)
On the formula of finding roots of quadratic function The detailed explanation of this formula, each step is written out, in order
In this question, only one 2 can be raised in the radical
x±√(x^2+1)
A summary of the knowledge of quadratic function in Grade 9 and the formula for finding roots
In general, the relationship between the independent variable x and the dependent variable y is as follows: y = ax ^ 2 + BX + C (a, B, C are constants, a ≠ 0, and a determines the opening direction of the function. When a > 0, the opening direction is upward; when a < 0, the opening direction is downward. IAI can also determine the opening size. The larger the IAI, the smaller the opening, The smaller IAI is, the larger the opening is. The right side of the quadratic function expression is usually a quadratic trinomial. II. The three general expressions of quadratic function: y = ax ^ 2; + BX + C (a, B, C are constants, a ≠ 0) vertex formula: y = a (X-H) ^ 2; + K [the vertex P (h, K)] intersection formula: y = a (x-x1) (x-x2) [only for parabola with intersection points a (x1,0) and B (x2,0)] Note: among the three forms of mutual transformation, there are the following relations: H = - B / 2a, k = (4ac-b ^ 2;) / 4A x1, X2 = (- B ± √ B ^ 2; - 4ac) / 2A III. the image of quadratic function is made into the image of quadratic function y = x? In plane rectangular coordinate system, The graph of quadratic function is a parabola. IV. the properties of parabola 1. Parabola is an axisymmetric graph. The symmetry axis is a straight line x = - B / 2A. The only intersection point between the symmetry axis and the parabola is the vertex P of the parabola. In particular, when B = 0, the symmetry axis of the parabola is the Y axis (i.e., the straight line x = 0). 2. The parabola has a vertex P, and the coordinate is p [- B / 2a, (4ac-b ^ 2;) / 4A]. When - B / 2A = 0, the parabola has a vertex p, and the coordinate is p [- B / 2a, (4ac-b ^ 2;) / 4A], When a > 0, the parabola opens up; when a < 0, the parabola opens downward. 4. The coefficient b of the first order and the coefficient a of the quadratic term jointly determine the position of the axis of symmetry, 5. The constant term C determines the intersection point between parabola and y-axis. 6. When the number of intersections between parabola and x-axis is Δ = B ^ 2-4ac > 0, there are two intersections between parabola and x-axis. When Δ = B ^ 2-4ac = 0, there is one intersection point between parabola and x-axis, There is no intersection point between the parabola and the x-axis.v.the quadratic function and the quadratic equation of one variable, in particular, the quadratic function (hereinafter called the function) y = ax ^ 2; + BX + C, when y = 0, the quadratic function is a quadratic equation of one variable with respect to X (hereinafter called the equation), namely ax ^ 2; + BX + C = 0, The abscissa of the intersection point between the function image and the x-axis is the root of the equation. When the parabola y = AX2 is drawn, the list should be listed first, then the points should be traced, and finally the line should be connected. The independent variable x value in the list is often centered on 0, and the integer value that is convenient for calculation and tracing points should be selected, There are several forms of the analytic formula of quadratic function: (1) general formula: y = AX2 + BX + C (a, B, C are constants, a ≠ 0); (2) vertex formula: y = a (X-H) 2 + K (a, h, K are constants, a ≠ 0). (3) two formulas: y = a (x-x1) (x-x2), where X1 and X2 are the abscissa of the intersection point of parabola and x-axis, namely the two roots of the quadratic equation AX2 + BX + C = 0, Note: (1) any quadratic function can be transformed into vertex formula y = a (X-H) 2 + K, the vertex coordinates of parabola is (h, K), when h = 0, the vertex of parabola y = AX2 + k is on the Y axis; when k = 0, the vertex of parabola a (X-H) 2 is on the X axis; when h = 0 and K = 0, the vertex of parabola y = AX2 is at the origin, Let y = ax ^ 2; if the symmetry axis is Y-axis but not the origin, then let y = ax ^ 2 + K define and define expressions. Generally, there is the following relationship between the independent variable x and the dependent variable y: y = ax ^ 2 + BX + C (a, B, C are constants, a ≠ 0, and a determines the opening direction of the function. When a > 0, the opening side is upward; when a < 0, the opening direction is downward, The smaller IAI is, the larger the opening is. The right side of the quadratic function expression is usually a quadratic trinomial. X is an independent variable and Y is a function of X. the three expressions of quadratic function are: y = ax ^ 2 + BX + C (a, B, C are constants, a ≠ 0) ② vertex formula [vertex P (h, K)]: y = a (X-H) ^ 2 + K ③ intersection type [only with X-axis a (x1,0) and B (X2, For the quadratic function y = ax ^ 2 + BX + C, the vertex coordinates are (- B / 2a, (4ac-b ^ 2) / 4A), that is h = - B / 2A = (x1 + x2) / 2K = (4ac-b ^ 2) / 4A). ② the relationship between general formula and intersection formula x1, X2 = [- B ± √ (b ^ 2-4ac)] / 2A
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