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kicyunya [14]
3 years ago
11

Complete the square to rewrite y = x2 + 6x + 3 in vertex form. Then state whether the vertex is a maximum or a minimum and give

its coordinates.
A. Maximum at (3, –6)
B. Minimum at (3, –6)
C. Minimum at (–3, –6)
D. Maximum at (–3, –6)
Mathematics
2 answers:
Sloan [31]3 years ago
4 0

Answer:

<h2>C. Minimum at (–3, –6)</h2>

Step-by-step explanation:

The given expression is:

y=x^{2}+6x+3

So, to complete the square, we first have to find the squared quotient between the second-term coefficient and 2, the add and subtract this number at the same time in the expression, like this:

b=6

(\frac{b}{2} )^{2}=(\frac{6}{2} )^{2}=9

Then,

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

Now, we just have to group the terms that can be factorized:

y=(x^{2}+6x+9)+3-9

Then, the factorization would be made using the squared root of x^{2} and 9, which is:

y=(x+3)^{2} +3-9

At the end, we just operate independent number outside the factorization:

y=(x+3)^{2} -6

So, according to the complete square of the expression, we can see that the vertex has coordinates (-3;-6), which is a minimum, because the squared coefficient is positive, that means the parabola is concave up.

The reason why the vertex has that coordinates is because the explicit expression of a parabola is:

y=(x-h)^{2} +k

Where (h;k) is vertex coordinates.

Therefore, the answer is C.

masha68 [24]3 years ago
3 0

y = x² + 6x + 3

y = x² + 6x + 9 - 6

y = (x + 3)² - 6

since the coefficient of x² is positive, then min at (-3,-6). the answer is C.

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