Question

Find the nature of the graph of the following quadratic equation in terms of which side it will open.

I. $y=x^2-8x$	a. open upward
II. $y=-2x^2+3$	b. open downward
III. $y=x^2-6x+4$	c. open right
	d. open left

• A. $I\to a,II\to b,III\to a$
• B. $I\to a,II\to c,III\to d$
• C. $I\to a,II\to a,III\to a$
• D. $I\to a,II\to b,III\to b$

Answer 1

The correct option is A $I\to a,II\to b,III\to a$

Comparing with standard quadratic equation $y=a{x}^2+bx+c,$ we get $a=1,b=-8,c=0$.
Since the leading coefficient $a=1>0$, hence the graph will open upwards.

Comparing with standard quadratic equation $y=a{x}^2+bx+c,$ we get $a=-2,b=0,c=3$.
Since the leading coefficient $a=-2<0,$ hence the graph will open downwards.

Comparing with standard quadratic equation $y=a{x}^2+bx+c,$ we get $a=1,b=-6,c=4$
Since the leading coefficient $a=1>0,$ hence the graph will open upward.