Quadratic functions

Question 1

When a function has been fully factorised, how can its roots be calculated?

Answer 1

By going through each set of brackets and finding the value(s) of x that make the bracket equal to zero

Question 2

How can x²+ax be written in completed square form, where a is a constant?

Answer 2

(x+0.5a)²-0.25a²

Question 3

How can one solve a quadratic equation x²+ax+b=0 by completing the square?

Answer 3

Subtract c to give x²+ax=-b. Then complete the square on the left hand side to give (x+0.5a)²-0.25a²=-b. After this, rearrange to give x=±√(0.25a²-b)-0.5a

Question 4

What does the graph of y=ax²+bx+c look like for a>0?

Answer 4

As x tends to infinity or minus infinity, y tends to infinity

Question 5

What does the graph of y=ax²+bx+c look like for a<0?

Answer 5

As x tends to infinity

or minus infinity, y tends to minus infinity

Question 6

How can the point where the graph of y=f(x) crosses the x axis be found?

Answer 6

By setting y equal to zero and solving for x

Question 7

How can the point where the graph of y=f(x) crosses the y axis be found?

Answer 7

It is at the point (0, f(0))

Question 8

What is the quadratic formula?

Answer 8

x=(-b±√(b²-4ac))/(2a)

Question 9

What is the discriminant of a quadratic expression ax²+bx+c?

Answer 9

b²-4ac

Question 10

If a quadratic exression’s discriminant is positive, what can be determined regarding the number of real roots?

Answer 10

There are two real roots

Question 11

If a quadratic exression’s discriminant is negative, what can be determined regarding the number of real roots?

Answer 11

There are no real roots

Question 12

If a quadratic exression’s discriminant is zero, what can be determined regarding the number of real roots?

Answer 12

There is one real root