Problem

Do these listed features agree with the same quadratic function? The equation is \(y=(x-2)(x-4)\), the graph has zeros at \(2\) and \(4\) with vertex \((3,-1)\), and the table includes the points \((2,0)\), \((3,-1)\), and \((4,0)\).

Three supplied representations: equation y equals (x minus 2)(x minus 4); a fully scaled graph with labeled zeros (2, 0) and (4, 0) and vertex (3, −1); and table points (2, 0), (3, −1), and (4, 0). No agreement conclusion is shown.

Big Picture

What this problem is really about

Agreement across an equation, graph, and table requires matching structure as well as a few values. We’ll derive the zeros, symmetry input, and vertex height from the equation, then test every supplied point and opening feature against the other representations.

Answer choices

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No, they do not match because with zeros at 2 and 4 the vertex should be at (3,1), not (3,-1).

No, they do not match because the same zeros could come from a different quadratic, so the graph and table cannot be confirmed from the equation.

No, they do not match because having zeros at 2 and 4 means the vertex must be at one of the zeros, so (3,-1) cannot be right.

Yes, they match because the equation has zeros at 2 and 4, and halfway between them is x=3 where y=-1.

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Do these listed features agree with the same quadratic function? The equation is \(y=(x-2)(x-4)\), the graph has zeros at \(2\) and \(4\) with vertex \((3,-1)\), and the table includes the points \((2,0)\), \((3,-1)\), and \((4,0)\).

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