The vertex of a parabola is (3,2). A second point on the parabola is (1,7). Which point is also on the parabola?

Answer choices include: (-1,7), (3,7), (5,7), and (3,-2)

1 Answer
Mar 13, 2018

(5,7)(5,7)

Explanation:

Method 1:
If you look at the graph, the only point that intersects the parabola is (5, 7)(5,7).
graph{5/4((x-3)^2)+2 [-4.5, 15.5, 0.16, 10.16]}

Method 2: Use the Vertex Form of parabolas to find the equation of the parabola:
y=a(x-h)^2+ky=a(xh)2+k
-> Use the provided values to plug into the equation.
y=a(x-3)^2+2y=a(x3)2+2
-> Solve for aa by plugging in (1,7)(1,7) into the equation.
7=a(1-3)^2+27=a(13)2+2
-> Solve for aa.
5=4a5=4a
a=5/4a=54
->Plug a into vertex form of parbola.
y=5/4(x-3)^2+2y=54(x3)2+2
-> Now, plug answer choices into the equation to see which one works with the equation.
-> Plug in 55 into the equation.
y=5/4(5-3)^2+2y=54(53)2+2
y=7y=7
-> Since y=7y=7 when you plug in 55, (5, 7)(5,7) is the correct answer. Hope this helps. :)