Question

function
the axis of symmetry for the function $f(x) = -2x^2 + 4x + 1$ is the line $x = 1$. where is the vertex of the function located?
$\bigcirc$ $(0, 1)$
$\bigcirc$ $(1, 3)$
$\bigcirc$ $(1, 7)$
$\bigcirc$ $(2, 1)$

Explanation:

Step1: Recall vertex on axis of symmetry

The vertex lies on the axis of symmetry \( x = 1 \), so the x - coordinate of the vertex is 1.

Step2: Substitute \( x = 1 \) into \( f(x) \)

Substitute \( x = 1 \) into \( f(x)=-2x^{2}+4x + 1 \):
\( f(1)=-2(1)^{2}+4(1)+1=-2 + 4+1=3 \)
So the vertex is at \( (1,3) \).

Answer:

B. (1, 3)