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

Answer:

C

Step-by-step 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:

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

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

Determine the x-coordinate of the vertex:

$\displaystyle x = -\frac{(2)}{2(-1)} = 1$

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.