Chapter 2 - Quadratics

Question 1

How do you solve a quadratic equation by factorising?

Answer 1

Write the equation in the form: ax² + 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 +/- square root of (b² - 4(ac)

2a

Question 3

What is the formula for completing the square?

Answer 3

x² + bx = (x + b/2)² - (b/2)²

Question 4

What is the domain?

Answer 4

The set of possible inputs for a function.

Question 5

What is the range?

Answer 5

The set of possible outputs for a function.

Question 6

What are the roots of a function.

Answer 6

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) = ax² + bx + c

Question 7

How do you find the turning point of a quadratic?

Answer 7

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 8

What does the value of the discriminant show?

Answer 8

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

Question 9

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

Answer 9

(b² - 4ac) > 0

Question 10

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

Answer 10

(b² - 4ac) = 0

Question 11

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

Answer 11

(b² - 4ac) < 0