Answer:
a=-5, k=31
Step-by-step explanation:
Determine a and k so the given points are on the graph of the function:
(1,11) (2,-14)
[tex]y=a(x+1)^2+k[/tex]
To find the required values, we substitute the points into the equation:
[tex]11=a(1+1)^2+k[/tex]
[tex]-14=a(2+1)^2+k[/tex]
Operating:
[tex]11=a(2)^2+k[/tex]
[tex]-14=a(3)^2+k[/tex]
Simplifying:
[tex]11=4a+k[/tex]
[tex]-14=9a+k[/tex]
Subtract the second equation from the first equation:
[tex]11+14=4a-9a[/tex]
Simplifying:
[tex]25=-5a[/tex]
Solving:
[tex]a=25/(-5)=-5[/tex]
a=-5
Use this equation to find k:
[tex]11=4a+k[/tex]
[tex]11=4(-5)+k[/tex]
[tex]11=-20+k[/tex]
k=31
a=-5, k=31
