Answered

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Find a quadratic function with the given vertex ans passing through the given point vertex forn E Vertex (4,5): passes through (1, 2)

Sagot :

The quadratic function forms a parabola. The vertex form of the equation is expressed as

y = a(x - h)^2 + k

Where

h and k are the x and y coordinates of the parabola's vertex. Given that the vertex is (4, 5),

h = 4, k = 5

Substituting these values into the above equation, it becomes

y = a(x - 4)^2 + 5

Given that the parabola passes through the point, (1, 2), we would substitute x = 1 and y = 2 into y = a(x - 4)^2 + 5. It becomes

2 = a(1 - 4)^2 + 5

2 = a * 9 + 5

2 = 9a + 5

9a = 2 -5

9a = - 3

a = - 3/9 = - 1/3

Substituting a = - 1/3 into y = a(x - 4)^2 + 5, the equation would be

[tex]y\text{ = -}\frac{1}{3}(x-4)^2\text{ + 5}[/tex]

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