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Sophie [7]
2 years ago
15

Please helpppp!!!!!!!!!!

Mathematics
1 answer:
masha68 [24]2 years ago
3 0

The vertex form of the quadratic function f(x) = x² + 2x + 3 is given as follows:

f(x) = (x + 1)² + 2

<h3>What is the equation of a parabola given it’s vertex?</h3>

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

In this problem, the function is:

f(x) = x² + 2x + 3

Completing the squares, we find the equation in vertex form, as follows:

f(x) = (x + 1)² + 2

As (x + 1)² = x² + 2x + 1, hence 2 has to be added to find the equivalent function.

More can be learned about quadratic functions at brainly.com/question/24737967

#SPJ1

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3 0
3 years ago
Determine the center and radius: x2 + y2 - 10x + 8y -8 = 0​
Kipish [7]

So our equation currently is ⇒ x^2+y^2-10x+8y-8 = 0

<u>Let's first move all the constant to one side and group 'like variables' together</u>:

      (x^2-10x)+(y^2+8y) = 8

<u>Now lets complete the square of both equations</u>

    (x^2-10x+25)+(y^2+8y +16) = 8 + 25 + 16\\(x-5)^2+(y+4)^2 = 49\\(x-5)^2+(y+4)^2 = 7^2

<u><em>Now we know the circle's general equation format is</em></u>:

   ⇒(x-h)^2+(y-k)^2 = r^2

  • (h, k) ⇒ coordinate of the center of the circle
  • r ⇒ length of radius of circle

<u>Thus the radius of the circle is 7</u>

<u></u>

Hope that helps!

7 0
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