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It is known that in the quadratic function y = AX2 + BX + C, the corresponding values of function y and independent variable X are shown in the following table X - 3 - 20135 y 708 - 9 - 57 find the function value y when the symmetry axis X = 2 of y = ax + BX + C
Three of them are taken into y = AX2 + BX + C. I calculate the function y = - 7x-10x + 8, and the axis of symmetry is - B / 2A = - 5 / 7. When x = 2, y = - 7 × 4-20 + 8, y = - 40
Given that the image of quadratic function y = AX2 + BX + C passes through three points a (- 4,0) B (0,2) C (- 2,0), the analytic expression of quadratic function is obtained
A:
The image of quadratic function y = AX2 + BX + C passes through three points a (- 4,0) B (0,2) C (- 2,0)
If the zeros are a and C, then the axis of symmetry x = (- 4-2) / 2 = - 3
Let y = a (x + 2) (x + 4)
The coordinates of point B are substituted into:
y(0)=a*2*4=8a=2
a=1/4
So: y = (x + 2) (x + 4) / 4
y=x²/4+3x/2+2
Given the quadratic function y = ax ^ 2 + BX + 1 (a ≠ 0), when x = 2, y = 1, when x = - 1, y = 2, then the coefficient of quadratic term is the coefficient of primary term
1=4a+2b+1, b=-2a
2=a-b+1 , b=a-1 , a=1/3 , b=-2/3
Given that the quadratic function f (x) = AX2 + BX + C (a > 0), there are two different intersections between the image and the X axis. If f (x) = 0, it is proved that 1 / A is the integral of the function f (x)
F (x) is equal to 0, so C is equal to 0. There are different intersections, so the discriminant B ^ 2-4ac is greater than 0
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