A function is shown f(x)=5(x-2)^2+3 what is the minimum value of the function

+ 3

Step-by-step explanation:

The equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = (x - 2)² + 3 ← is in vertex form

with vertex = (2, 3)

The minimum value occurs at the vertex and is the value of k

k = 3, thus minimum value is 3

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus