A biologist investigates the growth of a special flower. It is estimated that the height (in cm) of the flower is given by f(t) = at² + bt + C, where t is
the number of days passed since the start of the investigation. It is given
that the height of the flower first increases and then decreases.
What is the domain of f(t)?

The domain of this function is:

Domain f(t): t ≥ 0

or

Domain f(t): {x ∈ R | t ≥ 0}

Step-by-step explanation:

Given the function of the height (in cm) of the flower

f(t) = at² + bt + C

Here,

Given that height of the flower first increases and then decreases.

The current function represents the quadratic function because it is of the form. Hence, the graph would be a curve.

f(x) = ax²+ bx + c

where a, b and c are the real numbers and a≠0

Normally the domain of quadratic is the set of all real numbers, but here in this case x-values consist of the time in terms of the number of days.

As the time in terms of a number of days can not be negative. Therefore, we conclude that:

The domain of this function is:

Domain f(t): t ≥ 0

or

Domain f(t): {x ∈ R | t ≥ 0}

last one.

step-by-step explanation:

last one.

generally speaking, the others follow some sort of pattern that correlates to either linear (looks like a straight line) or sinusoidal (looks like an s).

the last one is just a random cloud of points that doesn't correlate to any particular known order.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct