SOLUTION: Can you tell me how to find the domain and range of this quadratic function? y = -2x^2 - x + 4 Thanks!

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Question 6693: Can you tell me how to find the domain and range of this quadratic function?
y = -2x^2 - x + 4
Thanks!
Answer by ichudov(507)   (Show Source): You can put this solution on YOUR website!
Since can be computed for every x (unlike, say, square root, which can only be computed for positive x), the domain is the entire set of real numbers.
The range can be guessed by looking at the graph

It has its maximum right in the middle between the roots, which is x = -b/2a, or . Now use substitution of into expression :
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: -2x^2-x+4 simplifies to 4.125
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( -2x^2-x+4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Replaced x with -0.25
It becomes .
Look at .
Replace constants in factor: highlight_red%28+-0.25+%29,highlight_red%28+2+%29 with highlight_green%28+0.0625+%29
It becomes .
Look at .
Replaced x with -0.25
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Factors 425 and 100 have greatest common factor (GCF) of 25. Reducing fraction.
It becomes .
Look at .
Replace constants in expression: highlight_red%28+-2%2A0.0625+%29,highlight_red%28+17%2F4+%29 with highlight_green%28+4.125+%29
It becomes .
Result:

Universal Simplifier and Solver


Done!


So, the domain is all numbers and the range is from minus infinity to 4.125.
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