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?

Answer 1

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?