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how do I find when two quadratic functions are at the same point by using the substitution method. here are the two equations:
y=-16x^2+150x+5 and y=54x+5 where x is measured in seconds

Sagot :

Panoyin
y = -16x² + 150x + 5
y = 54x + 5
  54x + 5 = -16x² + 150x + 5
- 54x                    -   54x       
            5 = -16x² + 96x + 5
         - 5                         - 5
            0 = -16x² + 96x
       16x² = -16x² + 16x² + 96
       16x² = 96
        16      16
           x² = 6
           x =+/-√(6)
y = -16(√(6)²) + 150√(6) + 5
y = -16(6) + 150√(6) + 5
y = -96 + 5 + 150√(6)
y = -91 + 150√(6)
(x, y) = (√(6), -91 + 150√(6))
or
y = -16(-√(6)²) + 150(-√(6)) + 5
y = -16(-6) + 150(-√(6)) + 5
y = 96 + 5  +150(-√(6))
y = 101 + 150(-√(6))
(x, y) = (-√(6), 101 + 150(-√(-6)))
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