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受欢迎的代数 >

4=a(2-h)^2+k,-4=a(-2-h)^2+k,5=a(1-h)^2+k

解答

4 = a (2 - h)^{2} + k, - 4 = a (- 2 - h)^{2} + k, 5 = a (1 - h)^{2} + k

解答

(h = 1, k = 5, a = - 1)

求解步骤

4 = a (2 - h)^{2} + k - 4 = a (- 2 - h)^{2} + k 5 = a (1 - h)^{2} + k

对于

4 = a (2 - h)^{2} + k

将

k

移到一边:

k = 4 - a (2 - h)^{2}

将

k = 4 - a (2 - h)^{2}

代入

- 4 = a (- 2 - h)^{2} + k

- 4 = a (- 2 - h)^{2} + (4 - a (2 - h)^{2})

化简

- 4 = 8 ha + 4

将

k = 4 - a (2 - h)^{2}

代入

5 = a (1 - h)^{2} + k

5 = a (1 - h)^{2} + (4 - a (2 - h)^{2})

化简

5 = 2 ha - 3 a + 4

解方程组:

- 4 = 8 ha + 4, 5 = 2 ha - 3 a + 4 : (h = 1, a = - 1)

将解代入原方程进行验证

因而，

4 = a (2 - h)^{2} + k, - 4 = a (- 2 - h)^{2} + k, 5 = a (1 - h)^{2} + k

最后的解是

(h = 1, k = 5, a = - 1)

流行的例子

x^{2} + 2 x = 2 x + 1

2 x^{2} - 9 x = 5 - 4 x

2 m^{2} + 4 m = 0

34=91.966x^2-180.82x+94.588

34 = 91.966 x^{2} - 180.82 x + 94.588

solvefor t,s=2t-t^2

so l v e f or t, s = 2 t - t^{2}