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

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

Answer from: Quest

answer: the answer is 30 miles per hour.

ft/s -> mphmph = ft/s 1.466667mph = 44 divided by 1.466667mph = 30.00000

- r3ktforgood ☕

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