Year 9 Quadratic Expressions And Non Linear Graphs

Question 1

What is a quadratic expression

Answer 1

A quadratic expression in x contains an x2 term, no higher powers of x.
Written in form ax2 + bx + c
a, b, c can be any any number but a cannot be 0

Question 2

Graph of a quadratic expression is called

Answer 2

Parabola

Question 3

Solve (x - 3)(x - 4)

Answer 3

.——-v—v
(x - 3)(x - 4)
*—^-^
= x2 - 4x - 3x + 12
= x2 - 7x + 12

Question 4

Solve (3x+ 1)(2x + 5y + 6)

Answer 4

.——-v——v—-v
(3x+ 1)(2x + 5y + 6)
*-^——^—-^
= 6x + 15xy + 18x + 2x + 5y + 6
= 26x + 15xy + 5y + 6

Question 5

Factorise x² + 9x + 20

Answer 5

(x )(x )
? x ? = 20
? + ? = 9
So, 4 x 5 = 20
And, 4 + 5 = 9
So it is (x + 4)(x + 5)

Question 6

How should the graph of a quadratic expression be drawn

Answer 6

No straight lines at parabola
Smooth unbroken curve at parabola / turning point.

Question 7

DOTS

Answer 7

Type of factorisation
Difference of 2 squares:
(x² - square number) = (x+√square number)(x-√square number)
(a²- b²) = (a+b)(a-b)

Example:
(x² - 9) = (x+3)(x-3)

(4x² - 16) = 4(x²-4) = 4(x+2)(x-2)

(4x² - 9) = (2x+3)(2x-3)