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) About Me  (Show Source):
You can put this solution on YOUR website!
Since -2x%5E2-x%2B4 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
graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+-2x%5E2-x%2B4%29+
It has its maximum right in the middle between the roots, which is x = -b/2a, or x=+-%28-1%29%2F%282%2A%28-2%29%29+=+-1%2F4. Now use substitution of x+=+-1%2F4 into expression -2x%5E2-x%2B4:
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Graphical form: -2x%5E2-x%2B4 simplifies to 4.125
  • Text form: -2x^2-x+4 simplifies to 4.125
  • Cartoon (animation) form: simplify_cartoon%28+-2x%5E2-x%2B4+%29
    For tutors: simplify_cartoon( -2x^2-x+4 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at -2%2Ahighlight_red%28+x+%29%5E2-x%2B4.
Replaced x with -0.25
It becomes -2%2Ahighlight_green%28+-0.25+%29%5E2-x%2B4.
Look at -2%2Ahighlight_red%28+-0.25+%29%5Ehighlight_red%28+2+%29-x%2B4.
Replace constants in factor: highlight_red%28+-0.25+%29,highlight_red%28+2+%29 with highlight_green%28+0.0625+%29
It becomes -2%2Ahighlight_green%28+0.0625+%29-x%2B4.
Look at -2%2A0.0625-highlight_red%28+x+%29%2B4.
Replaced x with -0.25
It becomes -2%2A0.0625-highlight_green%28+-0.25+%29%2B4.
Look at -2%2A0.0625-highlight_red%28+-0.25+%29%2Bhighlight_red%28+4+%29.
Added fractions or integers together
It becomes -2%2A0.0625%2Bhighlight_green%28+425%2F100+%29.
Look at -2%2A0.0625%2Bhighlight_red%28+425+%29%2Fhighlight_red%28+100+%29.
Factors 425 and 100 have greatest common factor (GCF) of 25. Reducing fraction.
It becomes -2%2A0.0625%2Bhighlight_green%28+17+%29%2Fhighlight_green%28+4+%29.
Look at -highlight_red%28+2%2A0.0625+%29%2Bhighlight_red%28+17%2F4+%29.
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 highlight_green%28+4.125+%29.
Result: 4.125

Universal Simplifier and Solver


Done!


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