The image shows a geometric representation of the function f(x) = x2 – 2x – 6 written in standard form.

1 answer:

7 0

The vertex form of the equation of a parabole is (x - h)^2 + k

So you must complete squares to transform x^2 -2x - 6 in its vertex form.

1) convert x^2 - 2x in a square => (x - 1)^2 - 1

2) Add the constant term - 6 => (x - 1)^2 -1 - 6

3) Add similar terms => (x - 1)^2 - 7

You can verify that (x - 1)^2 - 7 is equal to x^2 - 2x - 6:

x^2 - 2x + 1 - 7 = x^2 - 2x - 6. So, do not doubt it, the vertex form is (x - 1)^2 - 7, where the coordinates of the vertex are (1, - 7)

Answer: option A (x - 1)^2 - 7

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Question 27 Find the length of the hypotenuse. Leave answer in simplest radical form.

skelet666 [1.2K]

Use SOHCAHTOA. Since we are looking for the hypotenuse, you must use sine or cosine. Since, we are given the adjacent side, use cosine.

cosx=a/h

cos45=8/h

√2/2=8/h

*Cross multiply*

h√2=16

*Divide both sides by √2*

h=16/√2

*Multiply by √2/√2*

h=(16√2)/2

*Simplify the fraction*

h=8√2

Hope this helps!!

6 0

3 years ago

ASAP please help!!!

Serggg [28]

Y+4<9
subtract 4
y<5
y is smaller than and equal to 5
so you shade from 5 to the negative end to infinity (to the left) and shade the 5 to show that it is included (attachment says A)

6 less than (-6) 2 times a number (2 time x) is greater than (>) 8 (8)

-6+2x>8
add 6
2x>14
divide 2
x>7
so
x is bigger than 7
shade from 7 to the positive end to infinity (to the right) and don't shade 7 but put a circle around it to show that it is not included (attachment says B )

I have included pictures of the number lines