Question

f(x) = x2 + 7x + 9

(a) Write f(x) in the form k(x + t)2 + r. Fill in the obtained values of k, t, r:

k =

t =

r =

(b) Find the value of x where f(x) attains its minimum value or its maximum value.

x =

Answer 1

x^2+7x+9
\[(x+\frac{7}{2})^2-3.25\]so,
k=1
t=3.5
r=3.25

Answer 2

global min occurs at x=-7/2

Answer 3

f(x)=x^2 + 7x +9

by completing the sq,
f(x) = (x+7/2)^2 - (7/2)^2 +9
f(x) = (x+7/2)^2 - (13/4)

k=1, t=7/2, r=-13/4

since k=1, f(x) has a min value at
x+(7/2)=0
x=-7/2

when y is at -13/4, your vertex is (-7/2 , -13/4)