Mathematics, 17.07.2019 11:30 Geo777

Complete the square to rewrite y = x^2 + 6x + 3 in vertex form. then state whether the vertex is a maximum or a minimum and give its coordinates. a. maximum at (â€“3, â€“6) b. minimum at (3, â€“6) c. minimum at (â€“3, â€“6) d. maximum at (3, â€“6)

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Answer from: pollo44

First of all, we convert the equation to a vertex form.
$y = x^{2}+6x+3$
$y=(x^{2}+6x)+3$
$y = (x+3)^{2}+3-9
$
$y = (x+3)^{2}-6$ .
The equation in vertex form is $(x+3)^{2}-6$ . By looking at the equation we can understand that the y value of the vertex point is -6. By further calculation we can verify that the x value of the vertex point is -3.
Now, there are two ways of finding if the vertex point is a maximum or a minimum. The first way is picking random x coordinates after and before the y vertex value. If the values of y decrease before the y vertex point and increase afterwards, the vertex is a minimum. If the values of y increase before the y vertex point and then decrease afterwards, the vertex is a maximum point. The second way is applying teh second derivative. Here, I will show you the way of doing it:
$y = x^{2} + 6x +3$
$\frac{dy}{dx} = 2x + 6$
$\frac{d^{2}y}{dx^2} = 2$
The result proves two facts about the function:
1. The function has only one vertex/turning point.
2. The vertex/turning point is a minimum (due to the result of the second derivative being positive).

The answer is C.

Answer from: mikemurray115

vertex is (-3,-6)

Step-by-step explanation:

Complete the square to rewrite y = x^2 + 6x + 3 in vertex form.

In completing the square method, take the coefficient of middle term x

divide it by 2 and square it

6 divide by 2 is 3, 3^2=9

Add and subtract 9

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

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

Now we factor x^2+6x+9

y = (x+3)^2-6

The equation is in the form of y=a(x-h)^2+k , where (h,k) is the vertex

In our equation, h=-3 and k=-6

So vertex is (-3,-6)

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

percentage - 25%

probability - 0.25

we know,

total amount of students in class = 20

total boys = 10

total girls = 10

no of girls who wear glasses = 10/2 = 5

probability of choosing a girl with glasses is =

number of girls wearing glasses/total number of students in the class = 5/20

thus, percentage of selecting a girl wearing glasses will be

= 5/20 × 100

= 5 × 5

25%

therefore,

probability will be 0.25

happy to

pls mark as brainliest

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