Parabola a can be represented using the equation (x 3)2 = y, while line b can be represented using the equation y = mx 9. isabel claims one solution to the system of two equations must always be the vertex of parabola a. which best describes the reasonableness of her claim?

Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex. This can be obtained using finding y intercept of both parabolas and vertex of parabola A.

Is her claim correct?

Parabola A, (x + 3)² = y = x² + 6x + 9

Parabola B, y = mx + 9

For parabola A, when x = 0, y = (0+3)²

x=0, y = 9

y coordinate of parabola A is (0,9)

⇒The vertex coordinate,

(-b/2a , -(b²-4ac)/4a) = (-3,0)

For parabola B, when x = 0, y = 0 + 9

x=0, y = 9

y coordinate of parabola B is (0,9)

Isabel claims one solution to the system of two equations must always be the vertex of parabola A which is wrong.

Hence Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.

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Question: Parabola A can be represented using the equation (x + 3)2 = y, while line B can be represented using the equation y = mx + 9. Isabel claims one solution to the system of two equations must always be the vertex of parabola A. Which best describes the reasonableness of her claim?