Question

Easy math - lots of points

Answer 1

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)

$y=a(x+1)^2+k$

To find the required values, we substitute the points into the equation:

$11=a(1+1)^2+k$

$-14=a(2+1)^2+k$

Operating:

$11=a(2)^2+k$

$-14=a(3)^2+k$

Simplifying:

$11=4a+k$

$-14=9a+k$

Subtract the second equation from the first equation:

$11+14=4a-9a$

Simplifying:

$25=-5a$

Solving:

$a=25/(-5)=-5$

a=-5

Use this equation to find k:

$11=4a+k$

$11=4(-5)+k$

$11=-20+k$

k=31

a=-5, k=31