M - Pure 1 - 2) Quadratics

Question 1

Formula for the quadratic formula

Answer 1

x = [-b ± √(b² - 4ac)]/2a

Question 2

Equation for completing the square

Answer 2

ax² + bx + c → a(x + b/2)² - (b/2)² + c

Question 3

Name for the set of possible inputs and outputs of a function

Answer 3

• Inputs → domain
• Outputs → range

Question 4

Method to find the coordinates of the turning point on a quadratic graph

Answer 4

1. Complete the square in the form a(x + p)² + q
2. Turning point is at (-p, q)

Question 5

Method to find the coordinates of all critcal points on a graph, from a given function

Answer 5

• Crosses x-axis → find roots
• Y-intercept → set f(x) to 0
• Turning point → complete the square

Question 6

Information that the discriminant of a quadratic shows

Answer 6

• If b² - 4ac > 0 → has two distinct real roots
• If b² - 4ac = 0 → has one repeated real root
• If b² - 4ac < 0 → has no real roots