Respuesta :
The quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, -17) is [tex]-17(x-1)^{2}[/tex].
What is vertex form of a quadratic function?
The vertex form of a quadratic function is [tex]f(x) = a(x-h)^{2} + k[/tex] where a, h, and k are constants and (h, k ) is the vertex of the graph of the function.
According to the given question we have
The graph has the vertex is (1, 0) and passes through (2, -17)
Since, the general form of a quadratic function in a vertex form is
[tex]y = a(x-h)^{2}+ k[/tex]
substitute, h = 1 and k = 0 in the above equation
⇒ [tex]y = a(x-1)^{2} +(0)^{2}...(i)[/tex]
Also, the graph passes through the point (2, -17)
⇒ [tex]-17 = a(2-1)^{2}[/tex]
⇒ -17 = a or a = -17
Substitute the value of a in equation (i).
⇒[tex]y = -17(x-1)^{2}[/tex]
Therefore, the quadratic function in vertex form whose graph has the vertex (1, 0) and passes through the point (2, -17) is [tex]-17(x-1)^{2}[/tex].
Learn more about quadratic function in vertex form here:
https://brainly.com/question/13921516
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