The conditions of the relationship between root and coefficient in quadratic function Is it necessary that △ = b2-4ac be equal to 0?

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• 1. The relationship between quadratic function root and coefficient
• 2. A subject about quadratic function of relation between root and coefficient Given that a and B are two different roots of the equation x + x-2011 = 0, what is the square of the algebraic formula a + 2A + B equal to?
• 3. On quadratic function: using area to find analytic formula, using the relationship between root and coefficient to find analytic formula Example 1: given that the image of quadratic function y = ax ^ 2-4ax + B passes through a (1,0), B (x2,0), intersects with the positive half axis of Y axis and C point, and s Δ ABC = 2. Find the analytic expression of quadratic function Example 2: given that the parabola y = ax ^ 2-2ax-8a + 5 passes through the point P (- 2,5), intersects with the x-axis and a (x1,0), B (x2,0), X1 < X2, s △ PAB = 10, find the analytical formula of the parabola
• 4. The relationship between the root and coefficient of quadratic function Just forget the relationship, just say it, no proof
• 5. The relationship between the coefficient of quadratic term and coefficient of first term and constant term of quadratic function It's the relationship between a, B, C in y = ax'2 + BX = C and function image. Who can give me a full point, that is, what is greater than or less than. No difference~ It's the relationship between the image and a, B, C. for example, when B is less than or greater than 0, what are the characteristics of the image
• 6. Judge whether the following functions are quadratic functions. If they are quadratic functions, please state their quadratic coefficients, primary coefficients and constant terms （1）y=2x²-3； （2）y=3x-1； （3）y=（2x-1）（1-x）； （4）y=1/x²+1.
• 7. What is the coefficient of quadratic term, what is the coefficient of primary term and what is the constant term? Please explain it with a quadratic function
• 8. Write out the coefficient of quadratic term, coefficient of first term and constant term of quadratic function Coefficient of quadratic term and constant term of coefficient of primary term in function expression y=x2-2x-1 y=3x2+5 y=3x-1/2X2 y=2(x-1)(x+2) Y = (x-radical 2) 2-1
• 9. If the image of a quadratic function passes through the point (1,0) and the coefficient of the quadratic term of the analytic expression of the function is 1, then the analytic expression of the quadratic function is? (write one)
• 10. How to write image 2 of quadratic function
• 11. The relationship between quadratic function coefficients a, B, C and graphs
• 12. What is the effect of quadratic function coefficient B on function image When a and C are fixed, the influence of B on the image shape of quadratic function
• 13. How to judge the comparison of algebraic expressions with coefficients a, B and C according to the image of quadratic function
• 14. There is an image of a quadratic function. Three students have described some of its characteristics: A: the axis of symmetry is a straight line x = 4; B: the abscissa of the two intersections with the X axis is an integer, and the ordinate of the intersection with the Y axis is also an integer; C: the area product of the triangle with the three intersections as the vertex is 12______ ．
• 15. There is an image of a quadratic function. Three students have described some of its characteristics: A: the axis of symmetry is a straight line x = 4; B: the abscissa of the two intersections with the X axis is an integer, and the ordinate of the intersection with the Y axis is also an integer; C: the area product of the triangle with the three intersections as the vertex is 12______ ．
• 16. There is an image of a quadratic function. Three students have described some of its characteristics respectively: A: the axis of symmetry is a straight line x = 4; B: the abscissa of the two intersections with the X axis is an integer; C: the ordinate of the intersection with the Y axis is also an integer, and the triangular area product with the three intersections as the vertex is 24. Please determine an analytic formula of quadratic function that satisfies all the above characteristics
• 17. There is a quadratic function image, three students respectively said some of its characteristics: A: the axis of symmetry is a straight line x = 4 B: the abscissa of the intersection with the X axis is an integer C: the intersection with the Y axis is also an integer, and the area of the triangle with these three intersections as the vertex is 12+
• 18. There is a quadratic function image, three students respectively said some of its characteristics: A: the axis of symmetry is a straight line, x = 4; B: the abscissa of the intersection with the X axis is an integer C: the point of intersection with the Y axis is also an integer, and the area is 12
• 19. Please tell me how to solve this quadratic function, and how to find their quadratic function analytic expressions when the image passes through (1,0) (- 1,8) and (0,2)
• 20. Given the function f (x) = x (1 / (2 ^ x-1) + 1 / 2), ask: prove that it is even function