Q2. - Algebra 2

Question

Identify the vertex and the equation of the axis of symmetry for each function graphed below.

Step-by-Step Solution

Answer

      a. The equation of axis of symmetry is $x=2$ and the vertex is $\left(2,1\right).$

      b. The equation of axis of symmetry is $x=-3$ and the vertex is $\left(-3,-2\right)$.  

a Step 1. Use the concept.

All parabolas have an axis of symmetry. If you were to fold a parabola along its axis of symmetry, the portions of the parabola on either side of this line would match.

The point at which the axis of symmetry intersects a parabola is called the vertex.

Step 2. Given Information.

Step 3. Solution.

Clearly, the graph is symmetric around $x=2$ and the graph of parabola intersects the axis of symmetry at  $\left(2,1\right)$.

So, the equation of axis of symmetry is $x=2$ and the vertex is $\left(2,1\right)$.

b Step 1. Use the concept.

All parabolas have an axis of symmetry. If you were to fold a parabola along its axis of symmetry, the portions of the parabola on either side of this line would match.

The point at which the axis of symmetry intersects a parabola is called the vertex.

Step 2. Given Information.

The graph is:

Step 3. Solution.

Clearly, the graph is symmetric around $x=-3$ and the graph of parabola intersects the axis of symmetry at  $\left(-3,-2\right)$.

So, the equation of axis of symmetry is $x=-3$ and the vertex is $\left(-3,-2\right)$.