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.
<h3>Is her claim correct? </h3>
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?
