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Parabolas

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The parabolas defined by the equations y = x^2 + 4x + 6 and y = 2x^2 + 7x - 4 intersect at points and (a,b) and (c,d), where c >= a. What is c-a?

Nov 3, 2021

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The parabolas defined by the equations y = x^2 + 4x + 6 and y = 2x^2 + 7x - 4 intersect at points and (a,b) and (c,d), where c >= a. What is c-a?

$$y = x^2 + 4x + 6 \qquad and \qquad y = 2x^2 + 7x - 4$$

These are both concave up parabolas

Looking of  x values the points of intersection

$$x^2 + 4x + 6= 2x^2 + 7x - 4$$

solve that and you will get the 2 x values.

I will leave you to play with it now.

Nov 4, 2021