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NEED PRE CALC HELP WILL GIVE BRAINLIEST
1.) The path of two bumper cars can be represented by the functions 2x + y = –4 and y = x2 – x – 6. At which locations will the bumper cars hit one another?

2.)
If a nonlinear system of equations contains one linear function that never touches the quadratic function, then the system has which of the following?
No solution
One solution
Two solutions
Infinitely many solutions

Respuesta :

  • Solutions for a system of equations means finding out common points for the equations.
  • ( look attached file screenshot from Geogebra)

The solution is:

Point P ( -2 ; 0)

Point Q ( 1 ; -6)

2) If the linear equation never touches the quadratic function the system has no solution

The system:

2×x + y = -4           or    y = -4 - 2×x

y = x² - x - 6    (1)

Solving ( by substitution of  y value in equation (1)  )

- 4 - 2× x  =  x² - x - 6

x² - x - 6 + 4 + 2×x = 0

x² + x -2 = 0

Solving for x

x₁,₂ = ( - 1 ± √1 +8 ) / 2

x₁,₂ =  (-1 ± 3 )/2

x₁ = - 2

x₂ =  1

Now for x₁ = -2            y = (-2)² - ( -2) - 6     y =  0

Point P ( -2 ; 0)

For  x₂ = 1                    y = (1)² - ( 1) - 6          y = - 6

Point Q ( 1 ; -6)

Related Links: https://brainly.com/question/19130975

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