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 the left hand side
• set each factor equal to zero and solve to find the values of x

Question 2

how do you solve a quadratic equation using the quadratic formula?

Answer 2

• write the equation in the form: ax^2 + bx + c = 0
• identify the coefficients a, b and c
• use the formula:
  (-b ± √b^2 - 4ac)/2a

Question 3

how would you complete the square for the equation x^2 + bx?

Answer 3

(x + b/2)^2 - (b/2)^2

Question 4

how would you complete the square for the equation ax^2 + bx + c?

Answer 4

a(x+b/2a)^2 + (c-(b^2)/4a)

Question 5

what is the set of possible inputs for a function called?

Answer 5

the domain

Question 6

what is the set of possible outputs for a function called?

Answer 6

the range

Question 7

what are the roots of a function?

Answer 7

the values of x for which f(x) = 0

Question 8

what determines the shape of a quadratic graph?

Answer 8

the coefficient of x^2:
- if it is positive the parabola will be U shaped
- if it is negative the parabola will be ∩ shaped

Question 9

how can you find the turning point of a quadratic graph?

Answer 9

completing the square
if f(x) = a(x+p)^2 + q then the turning points would be at (-p, q)

Question 10

what is the discriminant?

Answer 10

the expression b^2 - 4ac (for a quadratic function)

Question 11

how does the discriminant show how many real roots f(x) has?

Answer 11

• if b^2 - 4ac > 0 then f(x) has 2 distinct real roots
• if b^2 - 4ac = 0 then f(x) has 1 distinct real root
• if b^2 - 4ac < 0 then f(x) has no distinct real roots