Mckenzie and cara both tried to find the missing side of the right triangle.
a right triangle is shown. one leg is labeled 5 and the other is labeled 13. a right angles is labeled in between the legs.

mckenzie's work cara's work
a2 + b2 = c2 a2 + b2 = c2
52 + 132 = c2 52 + b2 = 132
25 + 169 = c2 25 + b2 = 169
194 = c2 b2 = 144
square root 194 equals square root c squared. square root b squared equals square root 144.
13.93 ≈ c b ≈ 12

is either of them correct? explain your reasoning.

As we can see, Pythragorean Theorum is being applied in this situation. Pythagorean Theorum is when the sum of two legs of a triangle is equal to the hypotenuse, or the side that's across the right angle (90 degrees).
Pythagorean Theorum is defined in Mathematics by a^2 + b^2 = c^2.

One leg (a) is 5. The other leg (b) is 13.
Let's use Pythagorean Theorum.
5^2 + 13^2 = c^2
5 • 5 = 25
13 • 13 = 169
25 + 169 = 194.

Although the question isn't clearly defining who's correct, the person who chose "Square root 194 equals square root c squared" is correct.

I hope this helps. :)

Do you need with the x value for the minimum? its always between the two intercepts for a parabola