Question

The path of two bumper cars can be represented by the functions x + y = –5 and y = x2 – x – 6. At which locations will the bumper cars hit one another? (–1, –4) and (1, –6) (–2, 0) and (2, –4) (–2, 0) and (1, –6) (–1, –4) and (2, –4)

Answer 1

Equaling the equations, it is found that the cars hit each other at: (-1,-4) and (1,-6).

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For the first car, we have that:

$x + y = -5$

Thus:

$y_1 = -5 - x$

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For the second car:

$y_2 = x^2 - x - 6$

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They meet at the the values of x for which:

$y_1 = y_2$

Thus:

$-5 - x = x^2 - x - 6$

$x^2 - 1 = 0$

$x^2 = 1$

$x = \pm \sqrt{1}$

$x = \pm 1$

• When $x = 1$, they meet at $y = -5 - 1 = -6$
• When $x = -1$, they meet at $y = -5 - (-1) = -5 + 1 = -4$

Thus (-1,-4) and (1,-6).

A similar problem is given at brainly.com/question/13308311