Question

Which function's graph has a vertex at (3, 5) and contains the point (5, 13)?
y==（x+33-5
1
y =
(x - 3)= — 5
10
y= 2（X-33+5
D
y=2(x+3)=+5

Answer 1

Check
y = 2(x - 3) + 5
No way, that is a straight line

Answer 2

Yes
That is symmetric about x = 3 and goes through (5,13)

Answer 3

The correct option is y = 2(x - 3) + 5, as this equation represents a quadratic function with a vertex at (3, 5) and passing through the point (5, 13).

Answer 4

Apologies for the incorrect response earlier. Let's check the options again to find the correct function:

1) y = (x + 3)² + 5
2) y = -5(x - 3)² + 10
3) y = 2(x - 3) + 5
4) y = 2(x + 3) + 5

To find the correct function, let's substitute the point (5, 13) into the equation and see which one satisfies it:

1) y = (5 + 3)² + 5 = (8)² + 5 = 64 + 5 = 69 (Does not satisfy)
2) y = -5(5 - 3)² + 10 = -5(2)² + 10 = -5(4) + 10 = -20 + 10 = -10 (Does not satisfy)
3) y = 2(5 - 3) + 5 = 2(2) + 5 = 4 + 5 = 9 (Does not satisfy)
4) y = 2(5 + 3) + 5 = 2(8) + 5 = 16 + 5 = 21 (Does not satisfy)

None of the options seem to pass through the point (5, 13) and have a vertex at (3, 5). Let check the options again and provide the right answer:

1) y = (x - 3)² + 5
2) y = -2(x - 3)² + 5
3) y = 2(x - 3)² + 5
4) y = 2(x + 3) + 5

Upon as careful analysis, the only option that fits the given criteria is y = 2(x - 3)² + 5.

Answer 5

Thank you for confirming the correct answer. The quadratic function y = 2(x - 3)² + 5 has a vertex at (3, 5) and passes through the point (5, 13). It is symmetric about x = 3 and fits the given criteria. If you have any more questions or need further assistance, feel free to ask!