Chapter 4.1, Problem 54PPSE

Solution

a.

To Find: The axis of symmetry of the parabola of the given table.

The axis of symmetry are,

  $x=4\text{ and }x=2.5$

Given: The required table,

  

Explanation:

As the vertex of parabola is either maximum or minimum $y-$ value of the graph.

From the first table, the maximum $y-$ value is $1$ .

So, the axis of symmetry is $x=4$ .

From the second table, the minimum $y-$ value is $2$ . But it is repeating. It means minimum must be below 2.

So, the axis of symmetry is $x=2.5$ .

Thus, the axis of symmetry of the parabola $x=4\text{ and }x=2.5$ .

b.

To verify: The axis of symmetry of the parabola from the given table.

Given: The required table,

  

Explanation:

The axis of symmetry is $x=4$ of the first table.

Notice the table $y-$ value is 1 and it is minimum value of the graph.

The axis of symmetry is $x=2.5$ of the second table.

Notice the table $y-$ value is about less than 2 and it is minimum value of the graph.

c.

To verify: The axis of symmetry of the parabola from the given table.

Given: The required table,

  

Explanation:

The graph of first table data,

  

The equation is $y_1=-4x^2+32x-63$ .

Notice the graph the axis of symmetry is $x=4$ . It is same that calculated in part (a).

The graph of second table data,

  

The equation is $y_2=4x^2-20x+26$ .

Notice the graph the axis of symmetry is $x=2.5$ . It is same that calculated in part (a).