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luda_lava [24]
3 years ago
6

What is the quadratic function f(x)=x^2+6x-2 In vertex form?

Mathematics
2 answers:
Yuliya22 [10]3 years ago
6 0

Answer: Option D

f(x)=(x+3)^2 -k

Step-by-step explanation:

For a quadratic function of the form

ax ^ 2 + bx + c

The x coordinate of the vertice is:

x =-\frac{b}{2a}

In this case the function is:

f(x)=x^2+6x-2\\\\

So

a=1\\b=6\\c=-2

The x coordinate of the vertice is:

x=-\frac{6}{2*1}\\\\x=-3

The y coordinate of the vertice is:

f(-3) = (-3)^2 +6(-3) -2\\\\f(-3)=-11

The vertice is: (-3, -11)

The form e vertice for a quadratic equation is:

f(x)=(x-h)^2 +k

Where

the x coordinate of the vertice is h and the y coordinate of the vertice is k.

Then h=-3 and k =-11

Finally the equation f(x)=x^2+6x-2\\\\ in vertex form is:

f(x)=(x+3)^2 -k

Greeley [361]3 years ago
4 0

<u>Answer:</u>

The correct answer option is D. f(x) = (x + 3)² - 11.

<u>Step-by-step explanation:</u>

We know that the standard form of a quadratic function is given by:

y = ax² + bx + c

The vertex form of a parabola is given by

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

h = -b / 2a and k = f(h)

In the given equation f(x) = x² + 6x - 2

a = 1, b = 6 and c = -2

<u>Finding h:</u>

h = -6 / (2 × 1)

h = -6/2

h = -3

<u>Finding k:</u>

k = 1(-3)² + 6(-3) + 3

k = 9 - 18 - 2

k = -11

Therefore, the given quadratic function in vertex form: f(x) = (x + 3)² - 11

<u />

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aliina [53]

Answer:

3 people

Step-by-step explanation:

Because 40+40 =80 also equals 2 people so if they can only do 80 together then you would need another person even if its 6 more pounds then 80.

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4 0
3 years ago
What is the solution to the equation 9 cubed x ≈ 7?
yulyashka [42]

<u>Answer</u>

7/729


<u>Explanation</u>

The question requires to you to find the value of x.

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729 x = 7

x = 7/729

4 0
3 years ago
Mandy emptied the bags and put the candy into equal groups.How many candies were in each group?
alexira [117]

Answer:

25

Step-by-step explanation:

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Answer: 25.

3 0
2 years ago
Triangle ABC has side lengths a= 24, b= 40, and c= 55. What is the measure of angle C? 83.6° 116.2° 23.0° 40.7°
Harlamova29_29 [7]
<h3>Answer:  116.2°</h3>

Work Shown:

c^2 = a^2 + b^2 - 2ab\cos(C)\\\\55^2 = 24^2 + 40^2 - 2*24*40\cos(C)\\\\3025 = 576 + 1600 - 1920\cos(C)\\\\3025 = 2176 - 1920\cos(C)\\\\3025 - 2176  = -1920\cos(C)\\\\849  = -1920\cos(C)\\\\-1920\cos(C) = 849\\\\\cos(C) = (849)/(-1920)\\\\\cos(C) \approx -0.4421875\\\\C \approx \cos^{-1}(-0.4421875)\\\\C \approx 116.243535748231^{\circ}\\\\C \approx 116.2^{\circ}\\\\

The first equation is one of the three variations for the Law of Cosines.

Make sure your calculator is in degree mode.

5 0
2 years ago
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