Question

For the quadratic equation $a{x}^2+bx+c=0.$ Match the following graphs with the conditions given.

• A. $a>0,D=0$
• B. $a>0,D>0$
• C. $a>0,D<0$

Answer 1

Given: 1) In this graph parabola is opening upward which means $a$ is definitely greater than zero. And also it touches the $x-$axis which means only one root, $\Rightarrow D=0.$


2) In this graph parabola is opening upward which means $a>0.$ And also it cuts the $x-$ axis at 2 different points which means two different roots therefore $D>0.$


3) In this graph parabola is opening upward which means $a$ is definitely greater than zero. And also it neither touches nor cuts the $x-$axis which means no roots therefore $D<0.$