Chapter 2 - Quadratics

Question 1

How do you solve a quadratic equation by factorising?

Answer 1

Write the equation in the form:

ax^2 + bx + c = 0.

Factorise left hand side. e.g.

(x + 1) (x - 1)

Set each factor equal to zero and solve to find the value(s) of x.

Question 2

What is the quadratic formula?

Answer 2

X= -b +- /b^2 - 4(ac)
——————-
2a

Question 3

What is the formula for completing the square?

Answer 3

x^2 + bx =

( x + b )^2 - (b)^2
— —
2 2

Question 4

How do you solve a quadratic equation by completing the square?

Answer 4

ax^2 + bx + c =

a( x + b )^2 + ( c - b^2 )
— ——
2a 4a

Then solve for x from there.

Question 5

What is the domain?

Answer 5

The set of possible inputs for a function.

Question 6

What is the range?

Answer 6

The set of possible outputs for a function.

Question 7

What are the roots of a function.

Answer 7

The roots of a function are the values of x where:

f(x) = 0

these roots are where a polynomial line will cross the
x-axis.

an example of a function is:

f(x) = ax^2 + bx + c

Question 8

How do you find the turning point of a quadratic?

Answer 8

complete the square of that quadratic and put it into the form:

f(x) = a(x+p)^2 + q

The turning point is (-p,q)

Question 9

What does the value of the discriminant show?

Answer 9

It shows how many roots the function f(x) has.

Question 10

What is the formula for 2 real solutions of a function?

Answer 10

b^2 - 4(ac) > 0

Question 11

What is the formula for 1 real solution of a function?

Answer 11

b^2 - 4(ac) = 0

Question 12

What is the formula when there are no real solutions of a function?

Answer 12

b^2 - 4(ac) < 0

Question 13

What do you do when it says write in the form

A-B(x - C)^2?

Answer 13

Complete the square.

It is written in a different way but is the same as

a(x - b)^2 + c.