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When the parabola y = ax square + BX + C passes through one, two and three image limits, then When the parabola y = ax square + BX + C passes through one, two, three image limits, then A.a>0,b>0,c=0 B.a>0,b
A
What is the relationship between the value of C in quadratic function ax ^ 2 + BX + C and the intersection of parabola and Y axis
y=ax^2+bx+c
Let x = 0, then y = C, so
C is the ordinate of the intersection of the parabola and the y-axis
Absolutely right,
When the intersection of quadratic function y = AX2 + BX + C and X axis is y = 0, then when the function value y = 0, the value of X is the abscissa of the intersection of parabola and X axis
Find the intersection coordinates of y = x & # 178; - 2x-3 and X axis
If y = (x-3) (x + 1), then when y = O
X-3 = 0 or x + 1 = 0
We can find x = 3 or x = - 1
Given the quadratic function y = a (X-H) 2, when x = 2, there is a maximum value, and the image of this function passes through points (1, - 3), the relationship of this quadratic function is obtained, and it is pointed out that when x is the value, y increases with the increase of X
According to the meaning of the problem, y = a (X-2) 2, substituting (1, - 3) into a = - 3, so the analytic expression of quadratic function is y = - 3 (X-2) 2, because the symmetry axis of the parabola is a straight line x = 2, and the opening of the parabola is downward, so when x < 2, y increases with the increase of X
RELATED INFORMATIONS
- 1. The maximum value of quadratic function y = ax & # 178; + BX + C is 4, and the image passes through the point (- 3,0)
- 2. Given that the quadratic function y = ax & # 178; + BX + C has the maximum value and is negative, then a =?. C =?
- 3. As shown in the figure, it is known that the image of quadratic function y = AX2 + BX + C (a, B, C are real numbers, a ≠ 0) passes through point C (T, 2) and intersects with X axis at two points a and B. if AC ⊥ BC, then the value of a is______ ．
- 4. The vertex of the parabola y = ax's square + BX + C (a is not equal to 0) is m, and the focus of X axis is a and B (point B is on the right side of point a), △ ABM's three internal angles m and If the square of the quadratic equation (M-A) x with respect to x + 2bx + (M + a) = 0 has two equal real roots When the coordinates of vertex m are (- 2, - 1), find the analytical formula of the parabola and draw the general figure of the parabola;
- 5. The image of quadratic function y = ax ^ 2 + C passes through points a (1, - 3), B (- 2, - 6) Find this first-order function
- 6. As shown in the figure, it is known that the line y = KX + B intersects the parabola y = x2 ^ with P and Q, the abscissa of P is 2 and intersects the X axis with m (2,0) to find the expression of the line y = KX + B Find the area of the triangle formed by the point P, Q and the origin The abscissa of P is - 2
- 7. Given the parabola y = x square - (k-1) x-3k-2 and the x-axis image is called two points a (a, 0), B (B, 0), and a square + b square = 17, find K
- 8. Given that the parabola y = X2 - (k-1) x-3k-2 intersects the X axis at two points a (α, 0), B (β, 0), and α 2 + β 2 = 17, the value of K is obtained
- 9. The focus of parabola y = - x square + K and X axis is a (a, 0), B (B, 0). If a square + b square = 4, find the value of K
- 10. Given that the image of the function y = (K squared-k) x squared + KX + (K + 1) is a parabola, is the value range of K ≠ 1
- 11. It is known that the parabola and X-axis intersect at two points a-1,0, b1,0, and the analytic expression of the function is obtained through m0,1
- 12. If the parabola intersects the x-axis at points (2,0), (3,0) and the y-axis at points (0, - 4), then the expression of the quadratic function is________________ .
- 13. Given that the vertex coordinates of a parabola are (- 2,1) and pass through points (1, - 2), the analytic formula of the parabola is obtained
- 14. The parabola y = AX2 + BX + C passes through point a (3,0). B (2, - 3) with x = 1 as the symmetry axis Is there a point P on the symmetry axis X = 1 so that PA = Pb in the triangle PAB? If so, find out the coordinates of point P. if not, explain the reason
- 15. It is known that the image vertex coordinates of the quadratic function are a (- 2,0) and pass B (- 1,2) (find the analytic formula of the quadratic function, let the image intersect with the Y axis at point C, and find the area of △ ABC It is known that the image vertex coordinates of the quadratic function are a (- 2,0) and pass B (- 1,2) (1) to find the analytic formula of the quadratic function. (2) let the image intersect with the Y axis at point C, and find the area of △ ABC
- 16. The axis of symmetry of the parabola y = ax ^ 2 + BX + C is x = 2, passing through (0,4) and (5,9) Write down the whole process
- 17. As shown in the figure a (0,4) B (2,0), C is on the positive half axis of X axis, and the parabola y = AX2 + BX + C passes through ABC three points
- 18. Parabola y = 1 / 2x & # 178; + 1 can be regarded as parabola y = 1 / 2 (x + 3) &# 178; along X axis_ Translation_ Unit
- 19. When the parabola y = 2x-1 is translated upward by 2 units, the analytic expression of the function is_
- 20. Y = 1 / 2x + 1, y = 1 / 2x & # 178; - 3 / 2x + 1 find a point m on the symmetry axis of the parabola to make the value of ▏ am-mc ▏ maximum. (a is the intersection of the parabola and the Y axis, BC is the intersection of parabola and X axis, B is on the left side of C)