Question 254212: Are the following functions linear, quadratic or neither of the two? Explain how you know.
- y=3x-5
- y=(3x-2)(x+6) Found 2 solutions by richwmiller, Edwin McCravy:Answer by richwmiller(17219) (Show Source):
"Linear" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 1.
"Quadratic" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 2.
"Cubic" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 3.
"Quartic" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 4.
"Quintic" means that the largest exponent of x after the right side
is multiplied out and all like terms collected is 5.
But right now you're only studying the first two, "linear" and "quadratic"
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That doesn't need to be multiplied out or any terms collected.
And the largest power of x is 1, so it's linear.
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That needs to be multiplied out and like terms collected:
Use FOIL to multiply it out:
Collect like terms:
The largest power of x is 2, so it's quadratic.
[Note: You probably could just have looked at it and seen
that the largest power of x would end up being be 2 if you
multiplied it out and collected like terms without actually
bothering to to do so.]
Edwin
