Chapter 9.1, Problem 68HP

To determine

To formulate quadratic equation for which the axis of symmetry is $x=-\frac{3}{8}$ .

Answer to Problem 68HP

The quadratic function with axis of symmetry at $x=-\frac{3}{8}$ is $4x^2+3x+c$

Explanation of Solution

Given information :

The axis of symmetry is $x=-\frac{3}{8}$ .

Formula used :

The graph of a quadratic equation ( $y=a{x}^2+bx+c$ ) is a parabola. The parabola is symmetric in nature and the point of symmetry is known as the vertex. This vertex lies on the line of symmetry and is symmetric about this line.

The axis of symmetry bisects the parabola into two equal parts. Hence each point on the parabola would have an equal point on the other side of the axis of symmetry

Formula to compute equation of the axis of symmetry $x=-\frac{b}{2\times a}$ .

Axis of symmetry is

  $x=-\frac{3}{8}$

Calculation :

Equating the two equations above.

  $-\frac{b}{2\times a}=-\frac{3}{8}$

Simplifying the expression.

  $8b=6a$

The above expression holds true by putting $a=4\text{ and }b=3$

  $a{x}^2+bx+c$

In quadratic form,

  $4x^2+3x+c$

Therefore, the above expression gives a quadratic function with an axis of symmetry of $x=-\frac{3}{8}$ . Here c is any real number.