Ask questions, share knowledge, and connect with a vibrant community on IDNLearn.com. Our platform offers reliable and comprehensive answers to help you make informed decisions quickly and easily.
Sagot :
Given:
The graph passes through the given points (4,-2) and (2,0).
To find:
The quadratic function [tex]y=a(x-h)^2[/tex].
Solution:
We have, quadratic function
[tex]y=a(x-h)^2[/tex] ...(i)
The graph passes through the given points (4,-2) and (2,0). It means the equation must be true for these points.
Putting x=4 and y=-2 in (i), we get
[tex]-2=a(4-h)^2[/tex] ...(ii)
Putting x=2 and y=0 in (i), we get
[tex]0=a(2-h)^2[/tex] ...(iii)
Divide (iii) by (ii).
[tex]\dfrac{0}{-2}=\dfrac{a(2-h)^2}{a(4-h)^2}[/tex]
[tex]0=\dfrac{(2-h)^2}{(4-h)^2}[/tex]
[tex]0=(2-h)^2[/tex]
[tex]0=2-h[/tex]
[tex]h=2[/tex]
Putting h=2 in (ii), we get
[tex]-2=a(4-2)^2[/tex]
[tex]-2=a(2)^2[/tex]
[tex]-2=a(4)[/tex]
Divide both sides by 4.
[tex]\dfrac{-2}{4}=a[/tex]
[tex]\dfrac{-1}{2}=a[/tex]
Putting [tex]a=-\dfrac{1}{2}[/tex] and h=2 in (i), we get
[tex]y=-\dfrac{1}{2}(x-2)^2[/tex]
Therefore, the required quadratic function is [tex]y=-\dfrac{1}{2}(x-2)^2[/tex].
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.
