Question

6 multiple choice 1 point if the graph has point symmetry identify the point of symmetry, or if the graph has line symmetry identify the line of symmetry. x = - 4 x = 1 y = - 4 (0, - 3) (1, - 4)

Explanation:

Step1: Recall the definition of line symmetry

A graph has line symmetry if there is a line such that when the graph is folded along that line, the two halves match exactly.

Step2: Analyze the given parabola

For a parabola \(y = ax^{2}+bx + c\), the line of symmetry is given by the formula \(x=-\frac{b}{2a}\). In the case of a parabola that is symmetric about a vertical line (since this is a parabola opening upwards/downwards), we can also visually check. If we take points on either side of a vertical line \(x = k\), for example, if we have a point \((x,y)\) on one side of the line \(x = k\), then the point \((2k - x,y)\) should be on the other side of the line.
Looking at the graph, if we consider the vertical line \(x = 1\):
Take a point on the left - hand side of the line \(x = 1\), say \(x=0\). The corresponding \(y\) - value. If we take \(x = 2\) (since \(2\times1-0=2\)), we can see from the graph that the \(y\) - values for \(x = 0\) and \(x = 2\) are related in a symmetric way.

Answer:

\(x = 1\)