Question

question 27 · 1 point
determine the axis of symmetry of the parabola whose graph is given below.

Explanation:

Step1: Recall axis of symmetry formula

For a parabola, the axis of symmetry is a vertical line that passes through the vertex. If the parabola intersects the x - axis at two points \((x_1,0)\) and \((x_2,0)\), the axis of symmetry is given by \(x=\frac{x_1 + x_2}{2}\).
From the graph, the parabola intersects the x - axis at \(x=- 5\) and \(x=-3\).

Step2: Calculate the axis of symmetry

Using the formula \(x=\frac{x_1 + x_2}{2}\), substitute \(x_1=-5\) and \(x_2 = - 3\).
\(x=\frac{-5+( - 3)}{2}=\frac{-8}{2}=-4\).
We can also observe the vertex of the parabola. The vertex of the parabola (the lowest point) has an x - coordinate of \(-4\), which is the axis of symmetry.

Answer:

The axis of symmetry of the parabola is \(x = - 4\)