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lana [24]
3 years ago
10

ALGEBRA 1, SEM. 2; PLEASE SHOW WORK f(x)=x2+4x+7 in vertex form

Mathematics
2 answers:
Elina [12.6K]3 years ago
5 0

f(x) = x^2 + 4x + 7

f(x) = x^2 + 4x + 4 + 3

f(x) = (x + 2)^2 + 3

Vertex (h, k) where h = - 2 and k = 3

So vertex (-2 , 3)

emmasim [6.3K]3 years ago
4 0

f(x)=x^2+4x+7 \\ f(x)=x^2+4x+4+3\\ f(x)=(x+2)^2+3

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LekaFEV [45]
B

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5 0
2 years ago
Openstudt what are the coordinates of the turning point for the function f(x) = (x − 2)3 + 1? (−2, −1) (−2, 1) (2, −1) (2, 1)
Dominik [7]

f(x) = (x - 2)^3 + 1

Find the derivative:-

f'(x) =   3(x -2)^2   This = 0 at the turning points:-

so 3(x - 2)^2 =  

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3 0
3 years ago
At a point on the ground 80 ft from the base of a tree, the distance to the top of the tree is 11 ft more than 2 times the heigh
Sergio039 [100]

Let h be the height of the tree and d the distance to the top of the tree from the point on the ground. Draw a diagram to visualize the situation:

Since the distance to the top of the tree is 11 ft more than two times the height, then:

d=2h+11

Use the Pythagorean Theorem to relate the length of the sides of the right triangle:

\begin{gathered} h^2+80^2=d^2 \\ \Rightarrow h^2+6400=(2h+11)^2 \\ \operatorname{\Rightarrow}h^2+6400=(2h)^2+2(11)(2h)+11^2 \\ \operatorname{\Rightarrow}h^2+6400=4h^2+44h+121 \end{gathered}

Notice that we have obtained a quadratic equation in terms of h. Write it in standard form and use the quadratic formula to solve for h:

\begin{gathered} \Rightarrow0=4h^2+44h+121-h^2-6400 \\ \Rightarrow0=4h^2-h^2+44h+121-6400 \\ \Rightarrow0=3h^2+44h-6279 \\ \Rightarrow3h^2+44h-6279=0 \\  \\ \Rightarrow h=\frac{-44\pm\sqrt{(44)^2-4(3)(-6279)}}{2(3)} \\  \\ \therefore h_1=39 \\ h_2=-53.666.. \end{gathered}

Since the height of the tree must be positive, the only solution is h=39ft. To the nearest foot, the height of the tree is 39.

Therefore, the height of the tree is 39 ft.

4 0
1 year ago
How to slove this: x-5/3=x-3/5
sladkih [1.3K]

Answer: There are no solutions.

Step-by-step explanation:  x - 5/3 = x - 3/5

                                               x + -5/3 = x + -3/5

                                              x + -5/3 - x = x + -3/5 - x

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                                              0 = 16/15

7 0
4 years ago
Whats the relationship between area and square units
stira [4]
Okie, when you are talking about area, you will have units of course! :-)
So, square units are the units in which describe the area. Let's take a rectangle slab of paper that is 2 inches by 4 inches. Yes, the answer is 8, but what are the units. It is inches squared! Squared units are the units of area.
I hope this helps :-)
7 0
3 years ago
Read 2 more answers
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