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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
The image of parabola y = x square - (k-1) x-3k-2 and X axis is called two points a (a, 0), B (B, 0),
Let a and B be the two roots of the equation x ^ 2 - (k-1) x-3k-2 = 0
Then (k-1) ^ 2 + 4 (3K + 2) > 0, that is k > - 1 or K
Given that the square of parabola y = x - (k-1) x-3k-2 and X axis are at two points a (a, 0) and B (B, 0), and the square of a + the square of B = 17, find the value of K
It's a quadratic function. It's hard,
The original question can be changed into
The solution of the equation x ^ 2 - (k-1) x-3k-2 = 0 (because y = 0 at the intersection) is x = a, x = B
According to Weida's theorem, a + B = - [- (k-1)] / 1 = k-1, a * b = (- 3K-2) / 1 = - 3K-2
a^2+b^2=(a+b)^2-2*a*b=(k-1)^2-2*（-3k-2）
a^2+b^2=17
(k-1)^2-2*（-3k-2）=17
k^2+4k-12=0
k=-6 k=2
If k = - 6, the original formula - (k-1) = - 7 - 3K-2 = 16
[-(k-1）]^2-4*(-3k-2)
Given that the parabola y = xsquare - (k-1) x-3k-2 intersects the X axis at a (a, 0) B (B, 0) and a square + b square = 11, then the value of K is?
Please write down the process
y=x^2-(k-1)x-3k-2
Intersection with X axis at a (a, 0) B (B, 0)
Then a and B are the following two parts of the equation x ^ 2 - (k-1) x-3k-2 = 0
So a + B = k-1
ab=-3k-2
And the discriminant is greater than 0
(k-1)^2-4(-3k-2)>0
k^2+10k+9>0
(k+1)(k+9)>0
k>-1,k-1,k
If the square of parabola y = x - (k-1) x-3k-2 intersects with X at points a (a, 0), B (B, 0) and the square of a + the square of B = 17, then K=______ .
This is the ninth grade on the function point of view to see the quadratic equation of one variable
Δ= (k - 1) ^ 2 + 4 (3K + 2) = k ^ 2 + 10K + 9 > = 0, k = - 1, a + B = k - 1, ab = - 3K-2 from a ^ 2 + B ^ 2 = 17, there is (a + b) ^ 2-2ab = 17 (k-1) ^ 2 + 2 (3K + 2) = 17, k = - 6 (rounding off) or K = 2, so k = 2
RELATED INFORMATIONS
- 1. 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
- 2. 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
- 3. 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
- 4. It is known that the image of the function y = KX + m intersects with the opening downward parabola y = ax & # 178; + BX + C at two points a (0,1) B (- 1,0) (1) Find the analytic expression of the function y = KX + M (2) If there is an intersection C between the parabola and the x-axis, and the length of the line AC is the root 5, the analytic expression of the quadratic function y = ax & # 178; + BX + C is obtained
- 5. If y = ax & # 178; + BX + C and X-axis intersection (- 2,0) (1,0), its shape and opening direction are the same as the parabola y = - X & # 178;, then the parabola analytical formula
- 6. The intersection of the parabola Yax & # 178; + BX + C (a > 0) and the x-axis is a (x1,0), B (x2,0). The solution set of X10 is the inequality ax & # 178; + BX + C < 0?
- 7. If we know that the image of a function y = ax + B passes through a point (2,1), then the description of parabola y = ax ^ 2-bx + 3 is correct If the image of a function y = ax + B passes through a point (2,1), then the parabola y = ax ^ 2-bx + 3 is described as follows: (1) passing through a fixed point (- 2,5); (2) the axis of symmetry can be x = 1; (3) passing through a fixed point (0,3), (4) when a > 0, the maximum value of the ordinate of the vertex is 3; (5) when a < 0, the minimum value of the ordinate of the vertex is 3, (6) It is possible that B = - 2A_________________ .）
- 8. If the image of a function y = ax + B passes through (- 2,1), then the image of a parabola y = ax2-bx + 3 passes through () A. （-2，1）B. （2，1）C. （2，-1）D. （-2，-1）
- 9. Let the distance between the parabola y = x ^ 2 + ax + A-2 and the two intersections of X axis be 2, then the value of a is?
- 10. The shortest distance from parabola x ^ 2 = y to straight line 2x-y-4 = 0 is? The answer is (3 root 5) / 5,
- 11. 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
- 12. The image of quadratic function y = ax ^ 2 + C passes through points a (1, - 3), B (- 2, - 6) Find this first-order function
- 13. 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;
- 14. 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______ ．
- 15. Given that the quadratic function y = ax & # 178; + BX + C has the maximum value and is negative, then a =?. C =?
- 16. The maximum value of quadratic function y = ax & # 178; + BX + C is 4, and the image passes through the point (- 3,0)
- 17. 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
- 18. 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
- 19. 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________________ .
- 20. 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