Question

graph each function by first writing it in vertex form. then give maximum or minimum of the function and identify its zeros.

1.) f(x)=x^2-6x+9
2.)f(x)=x^2-2x-3
3.f(x)=-7x^2-14x
4.)f(x)=3x^2-12x+9

Answer 1

the equation is already in general/standard form Ax^2 + By +C = 0
vertex form a(x-h)^2 + k = 0
the x coordinate is -b/2a let this be h
then find 2c -(b/2a)^2 let this be k

Answer 2

the maximun or minimum occurs when f(x) = 0
to identify zeros x = h and k = 0

Answer 3

1.) f(x)=x^2-6x+9
a =1, b = -6 and c= 9
-b/2a = -(-6)/2*1 = 3
f(3) = 3^2 -6*3 + 9 =0
f(x) = (x-3)^2
zero when x = 3

Answer 4

2.)f(x)=x^2-2x-3
a = 1 b = -2 c = -3
-b/2a = - - 2/2*1 = 1
k =-3 - 1^2 = -3 -1 =-4
f(x) =(x-1)^2 -4

when f(x) = 0 then (x-1)^2 =4
x -1 = +/- 2
x = 2 + 1 , x = -2 + 1
x = 3, -1

Answer 5

the y -coordinate of a parabola is f(-b/2a)

Answer 6

try the rest