Chapter 2: Quadratics

Question 1

How do you solve a quadratic?

Answer 1

• Write the equation in the form Ax^2 + Bx + C = 0
• Factorise the left hand side
• Solve for values of x

Question 2

What is the quadratic formula

Answer 2

-B plus or minus the square root of B^2 minus 4AC, all over 2A

Question 3

How do you complete the square?

Answer 3

• Half the integer value
• Then square the value and subtract it
• Include any extra integers.

Question 4

What does completing the square show you?

Answer 4

• To find the max/ min of a graph
• To find the rest values of x eg f(x) has one real root

Question 5

Formula for completing the square?

Answer 5

x^2 + Bx = (x + B/2)^2 - (B/2)^2

Question 6

Formula for completing the square with a number in front of the X ?

Answer 6

Ax^2 + Bx +C = A(x + B/2A)^2 + (C- B^2/4A)

Question 7

What does it mean when asked to find f(5) when f(x) = 2x - 10 ?

Answer 7

It means you just substitute whatever is in the bracket into wherever x is in the equation eg 2(5)-10 so f(5) is 0

Question 8

Define Parabola

Answer 8

The formal name given to a curved quadratic graph

Question 9

How do you find the turning point of a graph ?

Answer 9

If f(x) = A(x+ p)^2 + q, then the turning point will be (-p,q)

Question 10

If B^2 - 4AC is greater than 0…

Answer 10

The graph has two distinct real roots

Question 11

If B^2 - 4AC is less than 0…

Answer 11

The graph has no real roots

Question 12

If B^2 - 4AC = 0…

Answer 12

The graph has one repeated root