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If n people attend the seminar and every two people shake hands once, the analytic formula between the number of handshakes y and the number of participants n is____ It is____ function
Everyone shakes hands with the other N-1
N people are n (n-1)
Yes, the handshake is two people, so each handshake is counted twice
So y = n (n-1) / 2
It's a quadratic function
Given the image of quadratic function f (x) passing through points a (0, - 2), B (- 1,0), C (5 / 4,9 / 8)
1. Find the analytic expression of F (x)
2. Judge whether f (x) has the maximum or minimum value in its domain, and calculate it
3. Find the equation of symmetry axis of F (x)
Please write the detailed process, thank you
Solutions: (1) Let f (x) = ax & # - 178; + BX + C, and substitute a (0, - 2), B (- 1,0), C (5 / 4,9 / 8) into the function
{c=-2
a-b+c=0
(25/16)a+(5/4)b+c=9/8
The solution is: {a = 2
b=0
c=-2
The analytic expression of F (x) is f (x) = 2x & # 178; - 2
(2) The minimum value of F (x) is - 2
(3) The equation of axis of symmetry of F (x) is x = 0
It is known that the image of quadratic function y = f (x) passes through three points (0, - 8), (1,5), (3,7)
1, find the analytic expression 2 of F (x), find the zero point 3 of F (x), compare the size relationship between F (2) f (4), f (- 1) f (3), f (- 5) f (1), f (3) f (- 6) and zero
Let y = ax & # 178; + BX + C, according to the meaning of the topic, have C = - 8, a + B + C = 59A + 3B + C = 7, a = - 4, B = 17, C = - 8. Therefore, the analytic expression of 1. F (x) is y = - 4x & # 178; + 17x-8 2. The zero point of F (x) is (0, - 8) 3. F (2) f (4) = 10 * (- 4) = - 40 < 0, f (- 1
RELATED INFORMATIONS
- 1. If the image of quadratic function f (x) passes through point (0,0), and f (x +!) = f (x) + X + 1, find the analytic expression of F (x)
- 2. It is known that a parabola is obtained by translating the parabola y = ax & # 178; upward by three unit lengths, and the parabola passes through the point (1,0), and its function analytic formula is obtained
- 3. Given that the parabola y = ax square + BX + C satisfies the following conditions, find the analytic expression of the function (1) Image passing point (- 1. - 6) (1, - 2) (2.3) (2) Vertex coordinate (- 1. - 1) and passing point (0. - 3) (3) Intersection with X-axis (- 2.0) (4,0) and passing through point (1, - 9 / 2)
- 4. If the square-2x-1 = 0 of the quadratic equation NX has no real root, then the image of the linear function y = (n + 1) x-n does not pass through the image line
- 5. The set of intersection points between the image of function y = x + 1 and the image of function y = x * 2 + a (constant a ∈ R) is represented by enumeration Quick return
- 6. Function y = 3x + 2 image and y = 1 / X image intersection set
- 7. Function y = (SiNx + 1) / (1 + X & # 178;) why is this a bounded function? How to judge
- 8. The following equation is: y = the absolute value of X, the absolute value of y = x, 5x & # 178; - y = 0, X & # 178; - Y & # 178; = 0. Where the number of functions where y is x is () A.0 B.1 C.2 D.4
- 9. (2) given y = f (x) = x & # 178; - 2x + 3, when x ∈ [T, t + 1], find the maximum and minimum function values of the function
- 10. The known function f (x) = 2x-1 g (x) = {X & # 178;, X ≥ 0} (piecewise function) - 1, x < 0 Why do we need to find the norm of X again to find the analytic expression of G [f (x)] g（x）={x²，x≥0 } -1，x＜0
- 11. According to his experience, a retailer estimated that (3000-100x) toy dinosaurs could be sold if they were sold at the price of X yuan per dinosaur. It is known that the cost of toy dinosaurs is 20 yuan 1. Write the formula of Y represented by X 2. Judge how many yuan each toy dinosaur sells, y is the biggest
- 12. Find the analytic expression of quadratic function It is known that two points a (12,82) B (14,81) B are the vertices of the function, and the solution set with F (x) greater than 80 is obtained Wrong! Point a is the vertex.
- 13. It is known that the parabola passes through B (0,4) C (5,9) and its vertex falls on the positive half axis of X axis
- 14. Analytic expression of quadratic function in Mathematics 1. On the image of quadratic function y = ax ^ 2 + BX + C, there are two points whose coordinates are (3,5) and (2) (- 2,15), find the analytic expression of this function 2. On the image of quadratic function y = ax ^ 2 + BX + C, there are two points whose coordinates are (m, n) and (m, n) (P, q)
- 15. The undetermined coefficient method of quadratic function is used to find the analytic expression of quadratic function 1. (1,2), (3,0), (- 2,20) three-point coordinates, find the analytic expression of quadratic function
- 16. Some concepts of quadratic function Y = a (X-H) + K, if the vertex coordinates are (5,8) or (- 5, - 8) Can it be reduced to y = a (X-5) square + 8 or y = a (x + 5) square-8? What do h and K mean? Also, if you want to translate the parabola y = ax right or left n units respectively In y = a (x? H), which side is the addition and which side is the subtraction? Is the sign of H always the same?
- 17. According to the following conditions, the analytic expression of quadratic function is obtained: (1) the image of quadratic function passes through points (1,0), (- 1, - 6), (2,6); A + B + C = 0 - A-B + C = - 6, 4A + 2B + C = 6, add two forms to get C = - 3, then a + B = 3 and 4A + 2B = 9 can get a = 1.5, B = - 4.5
- 18. Find the analytic expression of quadratic function satisfying the following conditions (1) The abscissa of the intersection of the parabola and the X axis is - 5 and 1, and the intersection of the parabola and the Y axis is at the point (0,5) (2) There is only one common point (2,0) between the parabola and the x-axis, and it intersects the y-axis at the point (0,2) (3) When x = 2, the minimum value of y = - 4, and the image passes through the origin Give points for answers before 9 o'clock
- 19. The analytic expression of quadratic function is determined according to the condition, Over three points (1,0), (5,0) and (2, - 3) If we use the analytic expression of quadratic function, we can't solve it,
- 20. (of quadratic function) 1. State the opening direction, axis of symmetry and vertex coordinates of the following parabola ⑴,y=1/3(x-5/3)^2+2/3 ⑵,y=-0.7(x+1.2)^2-2.1 ⑶,y=15(x+10)^2+20 ⑷,y=-1/4(x-1/2)^2-3/4 2. The following functions are reduced to the form of y = a (X-H) ^ 2 by the collocation method (1)y=x^2+4+5 (2)y=2x^2+4x 3. The vertex coordinates of parabola y = - 12x2 + 2x + 4 are_______ The axis of symmetry is_______ ； 4. The maximum value of quadratic function y = AX2 + 4x + A is 3, and the value of a is obtained 5. If the coordinates of any three points on the image of a quadratic function are known, the general formula (a ≠ 0) is used to find the analytic formula 6. Given the parabola y = 4 (x-3) ^ 2-16, write its opening direction, axis of symmetry and vertex coordinates 7. Determine the opening direction of parabola according to vertex formula__ The axis of symmetry is____ The vertex coordinates are____ .