Find the vertex and axis of symmetry of the graph of the function.
-$$f ( x ) = - 4 x ^ { 2 } + 8 x$$
A) (1, 0); x = 1
B) (-1, 0); x = -1
C) (-1, 4); x = -1
D) (1, 4); x = 1

Question

Quizplus · Accepted Answer

The vertex form of a quadratic function is given by $ f(x) = a(x-h)^2 + k $, where (h, k) is the vertex. For the function $ f(x) = -4x^2 + 8x $, we can find the vertex using the formula $ h = -\frac{b}{2a} $. Here, $ a = -4 $ and $ b = 8 $, so $ h = -\frac{8}{2(-4)} = 1 $. Substituting $ x = 1 $ back into the function gives $ f(1) = -4(1)^2 + 8(1) = 4 $. Thus, the vertex is (1, 4), and the axis of symmetry is $ x = 1 $.

Find the Vertex and Axis of Symmetry of the Graph f(x)=−4x2+8xf ( x ) = - 4 x ^ { 2 } + 8 xf(x)=−4x2+8x

Find the Vertex and Axis of Symmetry of the Graph $f ( x ) = - 4 x ^ { 2 } + 8 x$