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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!
Parabola y = - 4 (x + 3) square, if__ x≤ -3__ When x ≥ - 3, the function value 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___ Left_ Translation___ 3__ Units get
It is known that the vertex coordinate e (1,0) of the parabola ax ^ 2 + BX + C and the intersection coordinate of Y axis are (0,1)
(1) , find the function relation of parabola. (y = x ^ 2-2x + 1)
(2) Let a and B be two moving points on the x-axis, and the distance AB is 4. Let ad be perpendicular to the x-axis, BC be perpendicular to the x-axis, and the parabola intersect D and C. let a coordinate (T, 0) and the area of the quadrilateral ABCD be s
1. Find the function relation between S and T, and find out what quadrilateral ABCD is when s is the smallest?
2. When s is the minimum, find a point P on the diagonal BD, which is the minimum perimeter of the triangle PAE, and find the coordinates of P
(1) Because the vertex coordinate e (1,0) let y = a (x-1) ^ 2, because the function passes through (0,1), so 1 = a (0-1) ^ 2, the solution is: a = 1, so y = (x-1) ^ 2, that is y = x ^ 2-2x + 1 (2) if point a (T, 0), then point B (T + 4,0), so point d (T, y) y = (t-1) ^ 2, point d (T, (t-1) ^ 2) the same as point C (T + 4, (T + 4-1) ^ 2), that is (T + 4, (...)
It is known that the parabola y is equal to AX square plus BX plus C, passing through (0,1), and the vertex coordinate is (2. - 1)
Let the analytic expression of quadratic function be y = a (X-2) ^ 2-1
Substituting (0,1) into
1=4a-1
Then a = 1 / 2
So y = 1 / 2 (X-2) ^ 2-1
=1/2*x^2-2x+1
I hope my answer can help you,
In the upper right corner of my answer, click [adopt answer],
The vertex of the parabola y equals ax square plus BX plus C is an intersection point of D (- 1,2) and Y axis between (- 2,0) (- 3,0),
Which is right
1.b 2-4ac
RELATED INFORMATIONS
- 1. The vertex of the parabola y = AX2 + BX + C is on the Y-axis and passes through two points - (- 1,3), (- 2,6)
- 2. 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?
- 3. 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
- 4. When a
- 5. If a ＜ 0, the vertex of the parabola y = x * + 2aX + 1 + 2A * is in the? Th quadrant
- 6. 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______ ．
- 7. If the distance from a point m on the parabola x ^ 2 = - 16y to the focus is 6, then the coordinate of M is
- 8. 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
- 9. Let a (x1, Y1), B (X2, Y2), then x1x2 =? Let a (x1, Y1) and B (X2, Y2) pass through the focus of the parabola (x ^ 2) = 4Y to make the chord AB, then what is X1 times x2? There is a process or a graph.
- 10. How to find the directrix and focus of parabola? How to find the known parabola, collimator and focus? It is how to deduce the focal point and collimator of a parabola, or how to deduce a parabola from the focal point and collimator, just as the elliptic standard equation is derived by arithmetic and algebra.
- 11. 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
- 12. 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?
- 13. Parabola y square = 20x find the Quasilinear equation and focus coordinates? Write the calculation process
- 14. 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 |
- 15. In △ ABC and △ def, ab = 4, BC = 5, AC = 8, de = 6, DF = 12 are known, then △ ABC is similar to △ def when EF = ()
- 16. 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
- 17. 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
- 18. 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
- 19. 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?
- 20. High school physics in the role of capacitors in the circuit, she will cause what impact