SOLUTION: Give an example of a quadratic function that has zeroes at x = 2 and x = -2, and that takes the value 0 when x = 2.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Give an example of a quadratic function that has zeroes at x = 2 and x = -2, and that takes the value 0 when x = 2.      Log On


   

Question 1209609: Give an example of a quadratic function that has zeroes at x = 2 and x = -2, and that takes the value 0 when x = 2.
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: Anything of the form y+=+a%28x-2%29%28x%2B2%29 where 'a' is a real number
One example is y+=+5%28x-2%29%28x%2B2%29 where a = 5.

Explanation

If the quadratic has x = 2 as a root, then x-2 = 0. This leads to (x-2) as a factor.
x = -2 as a root leads to (x+2) as a factor.

That explains the %28x-2%29%28x%2B2%29 portion.

It changes to a%28x-2%29%28x%2B2%29 so we can vertically stretch and compress the parabola.

Check out this Desmos graph.
https://www.desmos.com/calculator/bzmy0reizl
Move the slider around for parameter 'a' so you can see these changes.

Notes:
  • When a < 0, the parabola opens downward.
  • When a > 0, the parabola opens upward.
  • When a = 0, the graph is a flat horizontal line overlapping the x axis.
  • The portion "takes the value 0 when x = 2" is redundant since x = 2 is a root aka x intercept.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Give an example of a quadratic function that has zeroes at x = 2 and x = -2,
and that takes the value 0 when x = 2.
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The condition that  " a function takes the value 0 when  x = 2 "  is  IDENTICALLY  THE  SAME

as the condition  " x = 2  is a zero of the function ".


        They are not two different conditions - they are  THE  SAME  condition.


So,  EITHER  the problem's creator got lost in three pines,
OR  he deliberately wants the reader to get lost in the three pines,
what he carefully placed for the reader in his post.

Or,  as the third alternative,  he does not know elementary basic mathematical terminology
and does not understand clearly what he writes.


Normal practice would be to collect fines for such posts.