Answer:
Step-by-step explanation:
= x - 5 ( x ≥ 3 )
( )² = ( x - 5 )²
x - 3 = x² - 10x + 25
x² - 11x + 28 = 0
(x - 4)(x - 7) = 0
= 7
= 4
Check the answer:
1). x = 7
= 7 - 2
√4 = 2
2 = 2
2). x = 4
= 4 - 5
1 = - 1 (False statement) ⇒ x = 4 is an extraneous solution.
Add 5 to both sides
5-5+x/3=5-11
0+x/3=-6
x/3=-6
times both sides by 3
3x/3=-18
x=-18
One solution
The two (or more) equations would only intersect once
No solution
Lines never intersect
The lines are parallel
Infinite solutions
The lines are the exact same
That’s all the characteristics I know
The easiest way to find the vertex is to convert this standard form equation into vertex form, which is y = a(x - h)^2 + k.
Firstly, put x^2 - 10x into parentheses: y = (x^2 - 10x) + 30
Next, we want to make what's inside the parentheses a perfect square. To do that, we need to divide the x coefficient by 2 and square it. In this case, the result is 25. Add 25 inside the parentheses and subtract 25 outside of the parentheses: y = (x^2 - 10x + 25) + 30 - 25
Next, factor what's inside the parentheses and combine like terms outside of the parentheses, and your vertex form is: y = (x - 5)^2 + 5.
Now going back to the formula of the vertex form, y = a(x - h)^2 + k, the vertex is (h,k). Using our vertex equation, we can see that the vertex is (5,5).
