DETERMINE THE VERTEX AND THE X-INTERCEPT (or zeros) of
f(x) = (x-4)^2 - 9

Vertex: (4,-9) .      zeros: 7,1

Step-by-step explanation:

a(x-h)^2+k .   vertex is (h,k) so it's (4,-9) in this case.

(x-4)^2-9=0 .  

(x-4)(x-4)-9=0

(x^2-8x+16)-9=0

x^2-8x+7=0

(x-7)(x-1)=0

x-7=0 . x-1=0

x=7 .  x=1

step-by-step explanation:

for the free

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²