Question

given the following quadratic function, determine the axis of symmetry. $y = 6(x + 2)^2 + 4$ plot the line which represents the axis of symmetry (plot 2 points to create a line)

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a quadratic function is \( y = a(x - h)^2 + k \), where the axis of symmetry is the vertical line \( x = h \).

Step2: Identify \( h \) from given function

Given \( y = 6(x + 2)^2 + 4 \), we can rewrite \( (x + 2) \) as \( (x - (-2)) \). So, comparing with \( y = a(x - h)^2 + k \), we have \( h = -2 \).

Step3: Determine axis of symmetry

Thus, the axis of symmetry is \( x = -2 \). To plot this line, we can find two points on \( x = -2 \), for example, \( (-2, 0) \) and \( (-2, 4) \) (any \( y \)-values work as long as \( x = -2 \)).

Answer:

The axis of symmetry is the vertical line \( x = -2 \). To plot it, use points like \( (-2, 0) \) and \( (-2, 4) \) (or other points with \( x = -2 \)) to create the line.