Question

question 13 (1 point) the points (-3, 5) and (7, 5) are the same distance from the vertex of their parabola. what is the equation for the axis of symmetry of the parabola? a) x = -3 b) x = 0 c) x = 2 d) x = 5

Explanation:

Step1: Recall property of parabola

For a parabola, points equidistant from the vertex have a symmetry - axis that is the perpendicular bisector of the line - segment joining those points.

Step2: Find mid - point of the line segment

The line segment is between the points \((-3,5)\) and \((7,5)\). The formula for the mid - point of two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(x=\frac{x_1 + x_2}{2}\), \(y=\frac{y_1 + y_2}{2}\). Here, \(x_1=-3\), \(x_2 = 7\), \(y_1 = 5\), \(y_2 = 5\). So, \(x=\frac{-3 + 7}{2}=\frac{4}{2}=2\), \(y = 5\). The axis of symmetry of the parabola (a vertical line for a parabola opening up/down) is \(x = 2\) since the axis of symmetry passes through the mid - point of points with the same \(y\) - coordinate (equidistant from the vertex).

Answer:

c) \(x = 2\)