Question

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)

Answer 1

`(5,7)`

Explanation:

Method 1:
If you look at the graph, the only point that intersects the parabola is `(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+k`
-> Use the provided values to plug into the equation.
`y=a(x-3)^2+2`
-> Solve for `a` by plugging in `(1,7)` into the equation.
`7=a(1-3)^2+2`
-> Solve for `a`.
`5=4a`
`a=5/4`
->Plug a into vertex form of parbola.
`y=5/4(x-3)^2+2`
-> Now, plug answer choices into the equation to see which one works with the equation.
-> Plug in `5` into the equation.
`y=5/4(5-3)^2+2`
`y=7`
-> Since `y=7` when you plug in `5`, `(5, 7)` is the correct answer. Hope this helps. :)