SOLUTION: Determine the vertex of y=x^2-8x+22.

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Question 7495: Determine the vertex of y=x^2-8x+22.
Answer by ichudov(507)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -24 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -24 is + or - .

The solution is

Here's your graph:


the vertex is at the midpoint between roots (never mind that roots are complex, you can still add them and divide sum by half and get a real number). That midpoint is x=4. Calculate the value of x^2-8x+22 for x=4, and you would get the x and y value this way.
Solved by pluggable solver: SUBSTITUTION solver -- compute expression given values
Your Result:


YOUR ANSWER


  • Graphical form: simplifies to
  • Text form: x^2-8x+22 simplifies to 6
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( x^2-8x+22 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Replaced x with 4
It becomes .
Look at .
Replace constants in factor: highlight_red%28+4+%29,highlight_red%28+2+%29 with highlight_green%28+16+%29
It becomes .
Look at .
Replaced x with 4
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Added fractions or integers together
It becomes .
Result:

Universal Simplifier and Solver


Done!


Answer: x=4, y=6
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