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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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