What is the quadratic function f(x)=x^2+6x-2 in vertex form?
a: f(x)=(x-3)^2+7
b: f(x)=(x+3)^2+7
c: f(x)=(x-3)^2-11
d: f(x)=(x+3)^2-11

Option D

Step-by-step explanation:

For a quadratic function of the form

The x coordinate of the vertice is:

In this case the function is:

So

The x coordinate of the vertice is:

The y coordinate of the vertice is:

The vertice is: (-3, -11)

The form e vertice for a quadratic equation is:

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 in vertex form is:

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

Step-by-step explanation:

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

Finding h:

h = -6 / (2 × 1)

h = -6/2

h = -3

Finding k:

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

true

explanation:

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step-by-step explanation:

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