Chapter 9.1, Problem 68HP

To determine

To Write:

The quadratic function for which the graph has an axis of symmetry of $x=-\frac{3}{8}$ .

Answer to Problem 68HP

A quadratic function for which the axis of symmetry is $x=-\frac{3}{8}$ may be $y=4x^2+3x+2$ .

Explanation of Solution

Given Information:

Given axis of symmetry of the required quadratic function is $x=-\frac{3}{8}$ .

Concept Used :

• Quadratic Functions:
• Quadratic functions are non-linear and are of the form:

  $f(x)=a{x}^2+bx+c;a\ne 0$

This is the standard form of Quadratic function.

• Shape of the graph of a Quadratic function is called Parabola.
• Parabolas are symmetric about a central line called Axis Of Symmetry.
• The axis of symmetry intersects a parabola only at one point , called the Vertex.
• Axis of Symmetry: Passes through the vertex and divides the parabola into two congruent halves.

  $x=-\frac{b}{2a}$

Calculation:

Axis of symmetry is $x=-\frac{3}{8}$ and the equation of axis of symmetry is $\begin{array}{l}x=-\frac{b}{2a}\\ where\\ y=a{x}^2+bx+c\mathrm{................}[standard\_form\_of\_quadratic\_equation]\end{array}$

Comparing it with general equation of axis of symmetry ,

  $\begin{array}{l}x=-\frac{b}{2a}=-\frac{3}{8}=-\frac{3}{2(4)}\\ \Rightarrow a=4\\ and\\ b=3\end{array}$

Substituting the values of a = 4 , b = 3 and any value for c .

  $\begin{array}{l}y=a{x}^2+bx+c\mathrm{.................}[s\tan dard\_form]\\ y=4x^2+3x+\mathrm{2................}[a=4,b=3,c=2]\end{array}$

So, a quadratic function for which the axis of symmetry is $x=-\frac{3}{8}$ may be $y=4x^2+3x+2$ .