Question

A parabola whose equation is y = (x - 5)^2 - 2 has a vertex at _____.

(-5, -2)
(-5, 2)
(5, -2)
(5, 2)

Answer 1

(5, -2) because y=(x-5)^2-2 is really y=x^2-10x+23 after you foil then take the derivative which is y'=2x-10 solve for x and you get 5 then put 5 in the original equation and you get -2 so the answer is (5, -2)

Answer 2

Answer:

Option 3 - (5,-2)

Step-by-step explanation:

Given : A parabola whose equation is $y=(x-5)^2-2$

To find : The vertex of the parabola

Solution :

The general vertex form of parabola is  

$y=a(x-h)^2+k$

Where, (h,k) is the vertex of the function.

The given function is already in vertex form so we compare it with general form

$y=(x-5)^2-2$

a =1,  h=5 and k=-2  

So, The vertex of the given parabola is (h,k)=(5,-2)  

Therefore, Option 3 is correct.