Chapter 9, Problem 5MCQ

To determine

To state the axis of symmetry.

Answer to Problem 5MCQ

The axis of symmetry is $x=\frac{5}{2}$ .

Explanation of Solution

Given information :

Given equation is $y=x^2-5x+4$ .

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.

This vertex point shall be:

1. Highest point (if $a<0$) and be called the maximum. Here, the graph opens downwards.
2. Lowest point (if $a>0$) and be called the minimum. Here, the graph opens upwards.

Here, a is greater than zero, hence the parabola opens upwards, and has a minimum value.

A parabola always points to infinity, either negative or positive.

Axis of symmetry for the given function is

  $x=-\frac{b}{2\times a}$

Substituting the values from the given equation.

  $x=-\frac{(-5)}{2\times 1}$

Simplifying.

  $x=\frac{5}{2}$

Therefore, the axis of symmetry is $x=\frac{5}{2}$ .