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Look at the graph of this system of equations: y = - x2 + 1 and y = x2. At which approximate points are the two equations equal? There more than one answer.

A.(-0.7, 0.5)
B.(0.5, 0.7)
C.(0.7, 0.5)
D.(-0.5, 0.7)

User Resting
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1 Answer

6 votes

Answer:

option A and C, (-0.7, 0.5) and (0.7, 0.5)

Explanation:

The two equations are equal means, the points at which the two graphs meet.

In that case the x and y coordinates satisfy both the graphs.

let the coordinates at the intersection point be (a,b).

Inserting in first equation,


b = -a^(2) + 1

Inserting in second equation,


b = a^(2)

Inserting value of b from second to first equation, we get


b = -b + 1


b = (1)/(2) = 0.5

Now inserting the value of b second equation, we get


(1)/(2) = x^(2)


x = \sqrt{(1)/(2) } = +(1)/(1.414) or -(1)/(1.414)  = +0.7  or  -0.7

Thus points are, (-0.7, 0.5) and (0.7, 0.5)

User Xonico
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