Question

find the vertex of the function $f(x) = -x^2 + 2x + 3$.
a. $(0, 3)$
b. $(3, -2)$
c. $(1, 4)$
d. $(2, 0)$

Explanation:

Step1: Recall vertex formula for quadratic

For \( f(x)=ax^2 + bx + c \), vertex x - coordinate is \( x = -\frac{b}{2a} \). Here, \( a=-1 \), \( b = 2 \).
\( x=-\frac{2}{2\times(-1)} = 1 \)

Step2: Find y - coordinate of vertex

Substitute \( x = 1 \) into \( f(x)=-x^2+2x + 3 \).
\( f(1)=-(1)^2+2\times1 + 3=-1 + 2+3 = 4 \)
So vertex is \( (1,4) \).

Answer:

c. (1, 4)