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Kay [80]
2 years ago
15

Put the quadratic into vertex form and state the coordinates of the vertex. y= y= \,\,x^2-6x-3 x 2 −6x−3

Mathematics
1 answer:
enot [183]2 years ago
3 0

Answer:

y = (x - 3)^2 - 12

(3,-12)

Step-by-step explanation:

Given

y = x^2 - 6x - 3

Solving (a): In vertex form

The vertex form of an equation is:

y = a(x - h)^2 + k

To do this, we make use of completing the square method.

We have:

y = x^2 - 6x - 3

------------------------------------------------------------------

Take the coefficient of x (i.e. -6)

Divide by 2; -6/2 = -3

Square it: (-3)^2 = 9

Add and subtract the result to the equation

------------------------------------------------------------------

y = x^2 - 6x - 3

y = x^2 - 6x + 9 - 9 - 3

y = x^2 - 6x + 9 - 12

Factorize x^2 - 6x + 9

y = x^2 - 3x-3x + 9 - 12

y = x(x - 3)-3(x - 3) - 12

Factor out x - 3

y = (x - 3)(x - 3) - 12

Express as squares

y = (x - 3)^2 - 12

Hence, the vertex form of y = x^2 - 6x - 3 is: y = (x - 3)^2 - 12

Solving (b): State the coordinates of the vertex.

In y = a(x - h)^2 + k; the vertex is: (h,k)

The vertex of y = (x - 3)^2 - 12 will be (3,-12)

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30 points
igomit [66]
Since the rate of descent is a constant this is a linear equation and can be expressed as:

h=vt+b, where h=feet, v=slope or rate, b=y-intercept (y value when x=0 which is the initial height)

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3 years ago
How many 16th notes = a half note?
Ber [7]

Answer:

hi so read explanation

Step-by-step explanation:

four sixteenth notes

Four eighth notes equal one- half note in duration and eight eighth notes equal  one whole    note. Two sixteenth notes are to  equal one- eighth note in duration and four sixte enth notes equal one- quarter note in durations. hope dis helped

4 0
3 years ago
What number is q in the problem -8-q-10q=-9q+6
uranmaximum [27]
For this question you can say:
-8 -11q = -9q +6 
so now you can add +9q on both sides and +8 on both sides of the equation:
-11q + 9q = 8 + 6 
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I hope this is helpful
have a nice day
8 0
3 years ago
Read 2 more answers
15 is 9 more than j.
Zina [86]

Answer:

j = 6

Step-by-step explanation:

"Is" typically means equals. "More than" means it is added to.

So 15 equals j with 9 added to it.

15 = 9 + j

Now solve for j by subtracting 9 from both sides.

15 - 9 = j

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aalyn [17]
I know this is late and you probably got the answer but just in case its C. 5. :P
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