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求以下中四數學題解法和答案 (急)
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發問:
1. consider f(x)=x^2 + (k+1)x + k where k is a constant. if f(k) + f(-k)=4, find the values of k2. If g(x-1)=x^2 -3x +5 , find g(x)3. The figure shows the graph of the function y=x^2 -8x +k with the axis of symmetry x=4 a) find the value of k b) find the coordinates of the vertex c)... 顯示更多 1. consider f(x)=x^2 + (k+1)x + k where k is a constant. if f(k) + f(-k)=4, find the values of k 2. If g(x-1)=x^2 -3x +5 , find g(x) 3. The figure shows the graph of the function y=x^2 -8x +k with the axis of symmetry x=4 a) find the value of k b) find the coordinates of the vertex c) using the result of (b) , find the min.value of the function 4. The figure shows the graph of the function y=-x^2 +bx -5 The vertex of the graph is ( -3 , k) a) find the value of b b) find the value of k c) using the result of (b) , find the max.value of the function 5. In each of the following , find the maximum or minimum value of the quafratic function and the corresponding value of x by the algebraic method y=3+2x(5-x) 6. consider the function f(x)= 3x^2 + hx +k. The y-intercept of the graph of the function is -5. If f(-2)=-5 , find a) the values of h and k b) the min.value of f(x) and the corresponding value of x 7. In the figure , ABCD is a rectangle with perimeter 64cm . P,Q,R,S are the mid-point of AB,BC,CD,DA respectively . Let x cm be the length of the rectangle a) express the area of quadrilateral PQRS in terms of x b) find the maximum area of quadrilateral PQRS
最佳解答:
1.Consider f(x)=x^2+(k+1)x+k where k is a constant. Find the values of k if f(k)+f(-k)=4.f(k)=k^2+(k+1)k+k=2k^2+2kf(-k)=k^2-(k+1)k+k=02k^2+2k=4 => 0=k^2+k-2=(k-1)(k+2)k=1,-2........ans 2.Find g(x) if g(x-1)=x^2-3x+5.y=x-1 => x=y+1g(y)=(y+1)^2-3(y+1)+5=y^2+2y+1-3y-3+5=y^2-y+3=> g(X)=X^2-X+3........ans 3.The figure shows the graph of the function y=x^2-8x+k with the axis of symmetry x=4 (a) find the value of ky=x^2-8x+k=(x^2-8x+16)+k-16y+16-k=(x-4)^2Vetex=(4,k-16) => k=16........ans (b) find the coordinates of the vertexVetex=(4,0).......ans(c) using the result of (b) , find the min.value of the functionmin=y(4)=0.......ans 4.The figure shows the graph of the function y=-x^2+bx-5. The vertex of the graph is (-3,k)(a) find the value of by=-x^2+bx-5=-(x^2-bx+b^2/4)-5+b^2/4=-(x-b/2)^2+(b^2-20)/4y-(b^2-20)/4=-(x-b/2)^2Vetex=(b/2,(b^2-20)/4)=(-3,k)b/2=-3 => b=-6.........ans (b) find the value of kk=(b^2-20)/4=(36-20)/4=4.......ans (c) using the result of (b), find the max.value of the function max=y(b/2)=y(-3)=k=4..........ans 2013-02-18 15:11:48 補充： 5.In each of the following: find the maximum or minimum value of the quafratic function and the corresponding value of x by the algebraic method y=3+2x(5-x). y=-2x^2+10x+3 =-2(x^2-5x+25/4)+3+25/2 y-31/2=-2(x-5/2)^2 max=y(5/2)=31/2.......ans 2013-02-18 15:12:23 補充： 6.Consider the function f(x)=3x^2+hx+k. The y-intercept of the graph of the function is -5. If f(-2)=-5 , find (a) the values of h and k y-intercept=f(0)=k=-5...........ans f(-2)=3*4-2h-5=-5 => h=6........ans 2013-02-18 15:12:42 補充： (b) the min.value of f(x) and the corresponding value of x f(x)=3x^2+6x-5 =3(x^2+2x+1)-5+3 =3(x+1)^2-2 min=f(-1)=-2..........ans 2013-02-18 15:29:29 補充： 7.In the figure, ABCD is a rectangle with perimeter 64cm. P,Q,R,S are the mid-point of AB,BC,CD,DA respectively . Let x cm be the length of the rectangle (a) express the area of quadrilateral PQRS in terms of x x=AB=CD, 32-x=BC=DA y=area(PR)=x(32-x)/2 2013-02-18 15:30:01 補充： (b) find the maximum area of quadrilateral PQRS y=16x-x^2/2 =-(x^2-32x+256)/2+128 =-(x-16)^2/2+128 max=y(16)=128.........ans
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