Questions: f(x)=2(x-3)^2-4

Solution Steps

To analyze the function \( f(x) = 2(x-3)^2 - 4 \), we can find its vertex, axis of symmetry, and determine if it opens upwards or downwards. The vertex form of a quadratic function is \( a(x-h)^2 + k \), where \((h, k)\) is the vertex. Here, \( a = 2 \), \( h = 3 \), and \( k = -4 \).

The function \( f(x) = 2(x-3)^2 - 4 \) is in vertex form \( a(x-h)^2 + k \). The vertex is given by \((h, k)\).

• Here, \( h = 3 \) and \( k = -4 \).

Thus, the vertex is \((3, -4)\).

The axis of symmetry for a quadratic function in vertex form is \( x = h \).

• Therefore, the axis of symmetry is \( x = 3 \).

The coefficient \( a \) in the vertex form \( a(x-h)^2 + k \) determines the direction of the parabola.

• Since \( a = 2 \) and \( 2 > 0 \), the parabola opens upwards.

Final Answer