Question

Which of the following are the coordinates of the vertex of y = −x2 + 2x + 1? (2, 1) (1, –2) (1, 2) (–2, 1)

Answer 1

C

Explanation:

We want to determine the vertex of the quadratic equation:

`\displaystyle y = -x^2 + 2x + 1`

Recall that the vertex is given by the formulas:

`\displaystyle \text{Vertex} = \left(-(b)/(2a), f\left(-(b)/(2a)\right)\right)`

In this case, a = -1, b = 2, and c = 1.

Determine the x-coordinate of the vertex:

`\displaystyle x = -((2))/(2(-1)) = 1`

To determine the y-coordinate, evaluate the function at x = 1:

`\displaystyle \begin{aligned} y(1)&= -(1)^2 + 2(1) + 1 \\ &= 2\end{aligned}`

In conclusion, the vertex of the quadratic equation is (1, 2).

Hence, our answer is C.