Find the vertex and axis of symmetry of the graph of the function.
-$$f ( x ) = 4 x ^ { 2 } + 24 x - 1$$
A)vertex: (-3, 107); x = -3
B)vertex: (-3, -37); x = -3
C)vertex: (3, 107); x = 3
D)vertex: (3, 35); x = 3

Question

Quizplus · Accepted Answer

The vertex of a parabola in the form $f(x) = ax^2 + bx + c$ can be found using the formula $(- \frac{b}{2a}, f(- \frac{b}{2a}))$. Here, $a = 4$, $b = 24$, so the x-coordinate of the vertex is $- \frac{24}{2 \cdot 4} = -3$. Plugging $x = -3$ into the original equation gives the y-coordinate: $f(-3) = 4(-3)^2 + 24(-3) - 1 = 36 - 72 - 1 = -37$. Therefore, the vertex is $(-3, -37)$, and the axis of symmetry is $x = -3$.

Find the Vertex and Axis of Symmetry of the Graph f(x)=4x2+24x−1f ( x ) = 4 x ^ { 2 } + 24 x - 1f(x)=4x2+24x−1

Find the Vertex and Axis of Symmetry of the Graph $f ( x ) = 4 x ^ { 2 } + 24 x - 1$