Determine the vertex of the function f(x) = 2(x − 5)2 + 8

In this question, you're trying to find the vertex of the given equation:

2(x − 5)² + 8

In order to find the vertex, you would get the coordinates from the equation.

The equation is already in vertex form: y= a(x-h)² + k

You'll get your x coordinate from h and y coordinate from k

5 is in the place of h in your equation, so that will be your x coordinate.

8 is in the place of k in your equation, so that will be your y coordinate.

When you combine the coordinates together, you should get:

(5, 8)

This means that your vertex will be at (5,8)

(5,8)

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.