Question

The graph shows the function f(x).

What is the function's average rate of change from x = 6 to x = 10?



Let ​ f(x)=x2+14x+36 ​ .

What is the vertex form of f(x)?

What is the minimum value of f(x)?

Enter your answers in the boxes.
Vertex form: f(x)=

Minimum value of f(x): y =






A rectangular flower bed is enlarged so that its area increases by 24 ft². The enlarged flower bed is a rectangle and its area is x2+11x+24 ft².

What expressions represent the dimensions of the flower bed before the increase?

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A group of botanists observe four types of plants for one week.

Is each situation linear?

Select Yes or No for each statement.
Statement Yes No
Plant #1 grows 8 mm per day.
Plant #2 doubles its height each day.
Plant #3 triples its height each day.
Plant #4 is 1.25 times taller each day.

Answer 1

the function's average rate of change from x=6 to x = 10
x = 6 f(x)=1, x=10 f(x)=9
let be m the average rate, so m = f(10)-f(6) / 10-6 = 9-1/10-6= 8/4=2

Let ​ f(x)=x²+14x+36
the vertex form of f is y=a(x-h)² + k, where h= - b / 2a, and k=c - b²/4a
so the answer is f(x)=(x + 7)² + 36- 49/4 = (x + 7)² + 95/4

Minimum value of f(x): y = 1 (look at the graph), because the minimum value of f is (6, 1)

expressions represent the dimensions of the flower bed before the increase
let S1 the area before the increase
it was enlarged 24ft², so the area is S1+ 24 ft²=x2+11x+24 ft², so S1=x2+11x

S1=x2+11x=(x+11)x, the dimensions before were W=x+1, and L=x

Statement Yes No
Plant #1 grows 8 mm per day : Yes
Plant #2 doubles its height each day. No (y=2.2^x, x number of day)
Plant #3 triples its height each day. No
Plant #4 is 1.25 times taller each day.No (y=1.25x)