Question

find the vertex of the graph of the quadratic function. determine whether the graph opens upward or downward, find any intercepts, and sketch the graph.
$f(x) = -x^2 + 4x - 10$
the vertex is
(simplify your answer. type an ordered pair. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall vertex formula for quadratic

For \( f(x) = ax^2 + bx + c \), vertex x - coordinate is \( x = -\frac{b}{2a} \). Here, \( a = -1 \), \( b = 4 \).
\( x = -\frac{4}{2\times(-1)} = 2 \)

Step2: Find y - coordinate

Substitute \( x = 2 \) into \( f(x) = -x^2 + 4x - 10 \).
\( f(2) = -(2)^2 + 4\times2 - 10 = -4 + 8 - 10 = -6 \)

Answer:

\((2, -6)\)