quadratic graphs

Question 1

how do we determine the shape of the quadratic graph

Answer 1

the co-efficient of the x

positive then it is a positive graph and turning point is a minimum

if it is negative then it is a negative graph and the turning point is a maximum

Question 2

how to find the co-ordinates of the turning point if you have both the roots

Answer 2

the turning point x value is the midpoint of the two roots

Question 3

What is the discriminant

Answer 3

The (b-4ac) in the quadratic formula

Question 4

How the discriminant value link to how many roots a quadratic graph has

Answer 4

If the discriminant value is ZERO then there will be only one root ( a repeating root)

If the discriminant value is <0
Then the quadratic graph has no real solutions

If the discriminant has a value of >0 then the quadratic graph has 2 roots

Question 5

What would it mean if we said the graph had 0 roots

Answer 5

We would just set the discriminant b2-4ac <0
Then do just treat it like an inequality
Same for if it had two roots but would be >0
Same for one root but would be =0
Same for it has at least one root >=0