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# Parabolas

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The parabolas defined by the equations y = -x^2 - x + 3 and y = 2x^2 - 1 intersect at points (a, b) and (c, d), where c is greater than or equal to a. What is c - a? Express your answer as a common fraction.

Dec 30, 2021

#1
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You are only looking for the 'x' coordinates of the poits of intersection ....so

-x^2-x+3  =  2x^2-1

3x^2+x - 4 = 0          x = 1   and - 4/3 <===== you can finish

Dec 30, 2021
#2
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What is c - a?

Hello Guest!

$$-x^2 - x + 3 = 2x^2 - 1\\ \color{blue}3x^2+x-4=0$$

$${\color{blue}a=}\frac{-1+7}{6}=\color{blue}1\\ b=1\\ {\color{blue}c=}2\cdot \frac{16}{9}-1=\color{blue}\frac{23}{9}\\ d=\frac{-1-7}{6}=-\frac{4}{3}\\$$

$$c-a=\frac{14}{9}$$

!

Dec 30, 2021