Problem 265

Problem 265

Sketch the graph of a quadratic function for which the related quadratic has one solution . Then, sketch one that has two solutions. Explain how you know by looking at the graph the number of solutions the are.

 

Solution

 

Now take two equations

One real solution  y=(x-3)²

Two real solution y=x²+3x+2

Graph for y=(x-3)²

 

 

Graph for y=x²+3x+2

 

 

Now from both graphs we can see in first graph

curve passes through a single point from x axis.

It means this equation has only one real solution.

And in second graph  curve cuts

the x- axis at two points

means this equation have two values of x