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6. If the parabola y = ax & # 178; + BX + C (a is not equal to 0) passes through the points a (- 1,0), B (3,0), then the symmetric axis of the parabola is a straight line, and the analytic function is?
x=1
It is known that the axis of symmetry of the parabola y = ax ^ 2 + BX + C (a is not equal to 0) is x = 1, and it passes through the points a (- 1,0), B (0. - 3), and the functional relationship corresponding to the parabola lock is obtained
Over b
x=0,y=0+0+c=-3
c=-3
Axis of symmetry x = - B / (2a) = 1
b=-2a
Over A0 = A-B + C
Then a + 2a-3 = 0
a=1
So y = x ^ 2-2x-3
The axis of symmetry of the parabola y = ax & # 178; - 2A & # 178; x-20a (a is not equal to 0) is
Straight line x = a
It is known that the parabola and X-axis intersect at points a (- 2,0), B (4,0), and the distance from vertex C to x-axis is 3. Find the functional expression of the parabola. Please write down the specific process and related knowledge points
Let y = a (x + 2) (x-4)
The abscissa of the vertex of the parabola is equal to the abscissa of the midpoint of a (- 2,0) and B (4,0), which is: (- 2 + 4) / 2 = 1
The coordinates of vertex C are (1,3) or (1, - 3)
When the vertex coordinates are C (1,3), we substitute x = 1, y = 3 to get:
a(1+2)(1-4)=3
-9a=3
a=-1/3
The analytical formula of parabola is y = (- 1 / 3) (x + 2) (x-4), and the general formula is y = (- 1 / 3) x & # 178; + (2 / 3) x + 8 / 3
When the vertex coordinates are C (1, - 3), we substitute x = 1, y = - 3 to get:
a(1+2)(1-4)=-3
-9a=-3
a=1/3
The analytical formula of parabola is y = (1 / 3) (x + 2) (x-4), and the general formula is y = (1 / 3) x & # 178; - (2 / 3) X-8 / 3
So the analytical formula of parabola is y = (- 1 / 3) x & # 178; + (2 / 3) x + 8 / 3 or y = (1 / 3) x & # 178; - (2 / 3) X-8 / 3
RELATED INFORMATIONS
- 1. The distance from the image vertex of quadratic function y = ax ^ 2 + K to the X axis is 3, and the shape is the same as that of parabola y = x ^ 2
- 2. Parabola y = - 4 (x + 3) square, when x_____ The value of function y increases with the increase of X_____ The value of function y decreases with the increase of X, and the square of parabola y = - 4 (x + 3) can be changed from the plane direction of parabola y = - 4x_____ Translation_____ Units get it!
- 3. The vertex of the parabola y = AX2 + BX + C is on the Y-axis and passes through two points - (- 1,3), (- 2,6)
- 4. Generally, we can use formula to find the vertex and symmetry axis of parabola y = ax ^ 2 + BX + C (a ≠ 0). Y = ax ^ 2 + BX + C = a [x + (B / 2a)] ^ 2+ Generally, we can find the vertex and symmetry axis of parabola y = ax ^ 2 + BX + C (a ≠ 0) y=ax^2 + bx + c =a[x+(b/2a)]^2 + (4ac-b^2)/4a, y=ax^2 + bx + c It should not be converted to (x + B / 2a) ^ 2 = B ^ 2-4ac / 4A ^ 2. How can it be converted to the above form?
- 5. It is known that the vertex m of the parabola y = AX2 + BX + C with downward opening is in the second quadrant And through the points a (1,0), B (0,1) (1) Please judge the value range of real number a and explain the reason (2) Let the other intersection of the parabola and the x-axis be c. when the area of △ AMC is 25 / 16 times of the area of △ ABC, a is obtained
- 6. When a
- 7. If a ＜ 0, the vertex of the parabola y = x * + 2aX + 1 + 2A * is in the? Th quadrant
- 8. Given that the distance from the point P on the parabola x2 = 4Y to the focus is 10, then the coordinate of point P is 0______ ．
- 9. If the distance from a point m on the parabola x ^ 2 = - 16y to the focus is 6, then the coordinate of M is
- 10. If the distance between a point P and its focus on the parabola x ^ 2 = 4Y is 2, then the distance between point P and its directrix is 2
- 11. Parabola y square = 20x find the Quasilinear equation and focus coordinates? Write the calculation process
- 12. If the vertex of the parabola is O, the focus is f, and M is the moving point on the parabola, then the value range of | Mo | / | MF |
- 13. In △ ABC and △ def, ab = 4, BC = 5, AC = 8, de = 6, DF = 12 are known, then △ ABC is similar to △ def when EF = ()
- 14. It is known that a straight line y = (K1-1) x + 2 and a hyperbola y = K2 / X intersect at two points a (2,4) and B. (1) find the coordinates of point B. (2) find the area of triangle AOB Please chop the proof of s △ AOB into Connect OA, ob
- 15. As shown in the figure, when we know the relationship between hyperbola y = K1 / X and straight line y = k2x. (1) k1k2, there are two intersections between straight line and hyperbola (2) If the line and hyperbola intersect at two points a and B, and the coordinates of point a are (1,2), the coordinates of point B are obtained (3) Are the two branches of hyperbola axisymmetric? If so, the expression of its axis of symmetry is given
- 16. In the circuit composed of voltmeter V, resistor R, capacitor C and key s, the electromotive force of the battery is ε, and the internal resistance is R. when the key s is connected stably () A. The reading of voltmeter is ε B. the reading of voltmeter is 0C. The voltage of capacitor is 0d. The voltage of capacitor is ε
- 17. Some questions about high school physics capacitor 1. In q = UC, u is the voltage across the capacitor So in a circuit, how to determine the voltage at both ends of the capacitor? 2. Is it possible to regard the resistance at both ends of a capacitor as a wire in any case? If not, under what circumstances can it be regarded as a wire? Under what circumstances can it not? 3. What is the role of the resistor in series with the capacitor? Does it affect the voltage at both ends of the capacitor? 4. Is a capacitor always considered open in a closed circuit?
- 18. High school physics in the role of capacitors in the circuit, she will cause what impact
- 19. A parallel plate capacitor is disconnected from the power supply after charging, and the negative plate is grounded After charging, a parallel plate capacitor is disconnected from the power supply, and the negative plate is grounded. A positive charge (small amount of charge) is fixed at point P between the two plates, as shown in the figure. E is the electric field strength between the two plates, u is the potential difference of the capacitor, and EP is the potential energy of the positive charge at point P. if the negative plate is kept stationary, move the positive plate to the position shown by the dotted line in the figure A. U becomes smaller, e remains unchanged, b.e becomes larger, EP becomes larger, c.u becomes smaller, EP remains unchanged, d.u remains unchanged, EP remains unchanged A I understand 1. What does this sentence mean when the negative plate is grounded 2. The explanation of C is that the electric potential does not change and the electric potential energy does not change Go to the position shown by the dotted line in the figure (move the positive plate downward)
- 20. The parallel plate capacitor is connected with the power supply after charging, and then the electrode plates are filled with isotropic uniform dielectric with relative permittivity of ε. How many times are the electric quantity on the two plates? How many times are the electric field strength? How many times are the electric field energy?