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

The solution to 4=a(2-h)^2+k,-4=a(-2-h)^2+k,5=a(1-h)^2+k is

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

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

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

Solution steps

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

Isolate

k

for

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

Plug

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

into

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

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

Simplify

- 4 = 8 ha + 4

Plug

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

into

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

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

Simplify

5 = 2 ha - 3 a + 4

Solve the system of equations:

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

Verify solutions by plugging them into the original equations

Therefore, the final solution for

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

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

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

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

2 m^{2} + 4 m = 0

3 u^{2} - 27 u = 0

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

What is 4=a(2-h)^2+k,-4=a(-2-h)^2+k,5=a(1-h)^2+k ?
The solution to 4=a(2-h)^2+k,-4=a(-2-h)^2+k,5=a(1-h)^2+k is