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It is known that the definition domain of quadratic function y = A & # 178; - 2a-1 is (- ∞, - 1) ∪ (3, + ∞) to find the minimum value of Y
Y = A & # 178; - 2a-1 = (A-1) ^ 2-2 the domain is (- ∞, - 1) ∪ (3, + ∞)
Axis of symmetry, x = 1
(- ∞, - 1] on the left side of the axis of symmetry, the function is a decreasing function
When x = - 1, y has the minimum value = 1 + 2-1 = 2
[3, + ∞) on the right side of the axis of symmetry, the function is an increasing function
When x = 3, y has a minimum value of 9-6-1 = 2
RELATED INFORMATIONS
- 1. Given that the minimum value of quadratic function y = x2 + (2a + 1) x + A2-1 is 0, then the value of a is () A. 34B. -34C. 54D. -54
- 2. Quadratic function y = a (x-1) &# B has the minimum value - 1, what is a + B The quadratic function y = a (x-1) &# 178; + B has a minimum value of - 1, what is a + B
- 3. The minimum value of quadratic function y = 15 (x-1) &# 178; is
- 4. It is known that the quadratic function y = x & # 178; + (2k-1) x + K & # 178; - 1 of X, if the sum of two squares of the quadratic equation x & # 178; + (2k-1) x + K & # 178; - 1 = 0 of X is 9, find the value of K and the vertex coordinates of the parabola, and find the correct vertex coordinates!
- 5. Given that the vertex coordinates of the quadratic function y = (a + 2) x & # 178; + A & # 178; - 1 are (0,3), then a=_____
- 6. What is the vertex coordinate of quadratic function y = (x-1) &# - 2?
- 7. The vertex coordinates of the image of quadratic function y = x & # 178; + 1 are
- 8. It is known that the quadratic function y = x square - (m square + 4) x-2m square-12 1. Verification: no matter what real number m takes, the parabola passes through a certain point, and the coordinates of the fixed point are obtained
- 9. Given that the image of the function f (x) defined on R is symmetric with respect to the point (- 3 / 4,0) and satisfies f (x) = - f (x + 3 / 2). F (- 1) = 1. F (o) = - 2, then the value of f (1) + F (2) + F (3) +... + F (2008) is () A.-2 B.-1 C.0 D.1
- 10. It is known that the image of the function f (x) defined on R is symmetric with respect to the point (- 3 / 4,0), satisfying f (x) = - f (x + 3 / 2), f (- 1) = 1, f (0) = - 2 Then the value of F (1) + F (2) +... + F (2008) is Please indicate the process
- 11. Quadratic function y = ax ^ 2 + BX + C The distance between the two intersection points of quadratic function y = ax ^ 2 + BX + C and X axis is 4 units. If the image is translated 1.5 units along the symmetric axis, then the image passes through the coordinate origin. If the original image is translated 2 units along the symmetric axis, then the image vertex is on the X axis, and the analytical formula of parabola is obtained
- 12. Given the quadratic function y = 3x-5x-2, when what is the value of X, y = 0, Y0
- 13. When B is a value, there is one intersection point between the primary function y = 5x + B and the secondary function y = x ^ 2 + 3x + 5, two intersections and no intersection point?
- 14. If there is an intersection between the image of the first function y = 5x + m and the image of the second function y = x2 + 3x + 5, then the value range of M is
- 15. How to draw the image of quadratic function? I see y = 3x ^ 2 confused How to establish? Told me. I will benefit a lot
- 16. Given that the image of quadratic function and a (- 1.4) are vertices and pass through point (2.5), the analytic expression of quadratic function is obtained,
- 17. The vertex (- 2,1) of quadratic function passes through the point (2,1), and the analytic expression of quadratic function is obtained
- 18. A formula for finding the vertex of quadratic function
- 19. What is the vertex formula of quadratic function? Vertex formula, not vertex formula The vertex formula is y = a (X-H) ^ 2 + K. I know, but I don't know how to match it. I need a formula
- 20. Which formula is used to find the analytic formula of the known vertex coordinates of quadratic function?