Chapter 9, Problem 5SGR

To determine

To state if true or false.

Answer to Problem 5SGR

False. A quadratic function with a graph that has two x- intercepts has two real roots.

Explanation of Solution

Given information :

A quadratic function with a graph that has two x- intercepts has two roots.

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.

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

To graph a quadratic equation using table of values, compute the ‘y’ values for the corresponding ‘x’ values. For this, substitute the values of ‘x’ with negative as well as positive integers and check for the vertex.

If the graph has two x- intercepts then it can be said that it has two real roots corresponding to the two x- coordinates of the intercepts. In other words, at y= 0 there are two real roots given by the corresponding x- intercepts.