If f(x) = 2x^2 - 3x + 2f(x)=2x2−3x+2, what is f(-2/3)f(−23)?

2 Answers
Zachary
Mar 20, 2018

44/9 or 4 8/9 or 4.88889449or489or4.88889 Because f(x)=2x^2-3x+2f(x)=2x2−3x+2, and f(-2/3)f(−23), this means -2/3−23 should be inserted for xx.

Explanation:

(-2/3)^2=(-2/3)*(-2/3)=4/9(−23)2=(−23)⋅(−23)=49
4/9*2=8/949⋅2=89
-3*(-2/3)=(-2*-3)/3=6/3=2−3⋅(−23)=−2⋅−33=63=2
2+2+8/9=4 8/9= 4.888892+2+89=489=4.88889

Aviv S.
Mar 20, 2018

f(-2/3)=44/9f(−23)=449

Explanation:

Simply plug in -2/3−23 for xx into f(x)f(x):

color(white)=f(-2/3)=f(−23)

=2(-2/3)^2-3(-2/3)+2=2(−23)2−3(−23)+2

=2((-2)^2/3^2)-3(-2/3)+2=2((−2)232)−3(−23)+2

=2(4/9)-3(-2/3)+2=2(49)−3(−23)+2

=(2*4)/9-3(-2/3)+2=2⋅49−3(−23)+2

=8/9-3(-2/3)+2=89−3(−23)+2

=8/9+3(2/3)+2=89+3(23)+2

=8/9+color(red)cancelcolor(black)3(2/color(red)cancelcolor(black)3)+2

=8/9+2+2

=8/9+4

=8/9+36/9

=8/9+36/9

=(8+36)/9

=44/9~~4.888889

We can use a calculator to check our work:

![https://www.desmos.com/calculator](useruploads.socratic.org)

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