IGCSE Quadratic Equations and Graphs

IGCSE Quadratic Equations and Graphs

Solve Quadratics

Identify features of Quadratic Graphs from the equation

Multiple Choice

Factorise the expression:

x² + 5x + 6

• (x + 3)(x + 2)

• (x + 2)(x - 3)

• (x + 5)(x + 1)

• (x - 2)(x - 3)

Multiple Choice

Factorise the expression:

x² - 2x - 24

• (x + 6)(x - 4)

• (x - 6)(x + 4)

• (x - 12)(x + 2)

• (x - 6)(x - 4)

Multiple Choice

Factorise the expression:

x² - 7x + 12

• (x + 3)(x + 4)

• (x - 3)(x - 4)

• (x - 3)(x + 4)

• (x + 3)(x - 4)

Multiple Choice

Factorise the expression:

x² + 9x + 20

• (x + 4)(x + 5)

• (x - 4)(x - 5)

• (x + 3)(x + 6)

• (x - 3)(x - 6)

Multiple Choice

Factorise the expression:

x² + x - 6

• (x + 3)(x - 2)

• (x + 2)(x - 3)

• (x + 6)(x - 1)

• (x + 1)(x - 6)

Quadratics

Quadratic expressions take the general form

 $ax^2+bx+c$  

When this expression is set = 0
we can solve the equation in several different ways.

Open Ended

Name as many techniques as you can that can be used to solve quadratics

Quadratics

 $ax^2+bx+c=0$  

can be solved by...

-Factorising

-Quadratic Formula

-Completing the Square

-Graphically

-Calculator

Multiple Choice

What are the solutions of this quadratic?

• -2 and 3

• -1/2 and -6

• -2 and -6

• 3 and -6

Multiple Choice

What are the solutions of this quadratic?

• x= 0 and x= -4

• x= 0 and x= 4

• y= 0

• x= 2

Multiple Choice

What are the solutions of this quadratic?

• -1 and -3

• 1 and -3

• 1 and 3

• -1 and 3

Multiple Choice

What should you do first in solving this equation?

x² + 6x - 13 = 3

• Get factored form

• Write down: a=1, b=6, c=-13

• Make it equal 0 by subtracting 3 on each side

• Type it all in a calculator.

Multiple Choice

In the equation

x² +5x +7 = 0

match each leading coefficient with its correct letter

• a=0, b=5, c=7

• a=1, b=5, c=7

• a=7, b=5, c=1

Multiple Choice

Identify the 'c' value:

16x² -8x -24 = 0

• 16

• -8

• 24

• -24

Multiple Choice

Use the quadratic formula to find the solutions for

y = 3x³ + 8x - 1

• 0.1167 and -2.7833

• 0.7 and -16.7

• 0.35 and -8.35

• 0.2358 and -1.236

Multiple Choice

Complete the Square

x² + 16x + 64

• (x+8)²

• (x-8)²

• (x-4)²

• (x+4)²

Multiple Choice

Complete the Square

x² + 12x + 64

• (x+6)²

• (x+6)²+18

• (x-3)²

• (x+6)²-18

Multiple Choice

Complete the Square

x² + 8x + 6

• (x+8)²

• (x+4)²+6

• (x+4)²-10

• (x+4)²+10

Multiple Choice

Solve the equation by completing the square:

 $x^2-2x-8=0$  

•  $x=\left\{-12,6\right\}$  

•  $x=\left\{-2,4\right\}$  

•  $x=\left\{4\right\}$  

•  $x=\left\{-4,\ 2\right\}$  

Multiple Choice

3x²+9x-30=0

• x= 2, -5

• x= 5, -2

• x= -5, -2

Multiple Choice

3x²-48=0

• x= 4, 4

• x= -4, -4

• x= -4, 4

Multiple Choice

6x²-x-2=0

• x= -2/3, 1/2

• x= 2/3, -1/2

• x= -2/3, -1/2

Quadratics

 $y=ax^2+bx+c$  

We can identify a lot about a Quadratic Graph from it's equation

- Curved shape - U if 'a' is positive

- Y-intercept - look at 'c'
- X-intercepts/roots - solve to find
-Turning point - complete the square

Multiple Choice

Is the value of 'a' positive or negative?

• Positive

• Negative

Multiple Choice

Is this Quadratic positive or negative?

• Positive

• Negative

Multiple Choice

Is this Quadratic positive or negative?

• Positive

• Negative

Multiple Choice

Is this Quadratic positive or negative?

• Positive

• Negative

Quadratics

 $y=ax^2+bx+c$  

We can identify a lot about a Quadratic Graph from it's equation

- Curved shape - U if 'a' is positive

- Y-intercept - look at 'c'
- X-intercepts/roots - solve to find
-Turning point - complete the square

Multiple Choice

What are the coordinates of the y-intercept of this quadratic?

y= x² + x - 6

• (-6, 0)

• (0,-6)

• (-2, 3)

• (2, -3)

Multiple Choice

What are the coordinates of the y-intercept of this quadratic?

y = x² -12x + 36

• (0,36)

• (0,-36)

• (0,-12)

• (0,12)

Multiple Choice

What are the coordinates of the y-intercept of this quadratic?

Y = -3x² +7x - 2

• (0,-3)

• (0, 7)

• (0,-2)

• (0, 3)

Multiple Choice

What are the coordinates of the y-intercept of this quadratic?

y = x² - 6x + 11?

• (0,11)

• (0,-6)

• (0,-11)

• (0,6)

Multiple Choice

What are the coordinates of the y-intercept of this quadratic?

y = (x+3)(x-5)?

• (0,3)

• (0,-5)

• (0,-15)

• (0,-2)

Multiple Choice

What are the coordinates of the y-intercept of this quadratic?

y = (x-9)(x-6)?

• (0,-15)

• (0,-9)

• (0,6)

• (0,54)

Quadratics

 $y=ax^2+bx+c$  

We can identify a lot about a Quadratic Graph from it's equation

- Curved shape - U if 'a' is positive

- Y-intercept - look at 'c'
- X-intercepts/roots - solve to find
-Turning point - complete the square

Multiple Choice

What are the roots of this quadratic

y= (x - 2)(x + 3)?

• x = - 2 or x = 3

• x = 2 or x = -3

• The are no real roots

• x = 2 or x = 3

Multiple Choice

What are the roots of this quadratic

y = x² + 16x + 63 ?

• x=7, x=4

• x=-7, x=9

• x=3, x=10

• x=-7, x=-9

Multiple Choice

What are the roots of this quadratic

y= x²+7x+10 ?

• x=-2, x=-5

• x=2, x=5

• x=-10, x=-4

• x=-2, x=5

Multiple Choice

What are the roots of this quadratic

y= x² -2x - 24 ?

• x=-4, x=6

• x=-4, x=-6

• x=-6, x=1

• x=4, x=-6

Quadratics

 $y=ax^2+bx+c$  

We can identify a lot about a Quadratic Graph from it's equation

- Curved shape - U if 'a' is positive

- Y-intercept - look at 'c'
- X-intercepts/roots - solve to find
-Turning point - complete the square

Multiple Choice

What is the coordinate of the turning point of this quadratic $y=\left(x+3\right)^2-2$  ?

• (-3, -2)

• (3, -2)

• (-3, 2)

• (3, 2)

Multiple Choice

What is the coordinate of the turning point of this quadratic $y=\left(x-3\right)^2-2$  ?

• (-3, -2)

• (3, -2)

• (-3, 2)

• (3, 2)

Multiple Choice

What is the coordinate of the turning point of this quadratic $y=\left(x-5\right)^2+8$  ?

• (-5, 8)

• (-5, -8)

• (5, 8)

• (5, -8)

Multiple Choice

What is the coordinate of the turning point of this quadratic $y=x^2+8x+10$  ?

• (8, 10)

• (-8, 10)

• (-4, -6)

• (4, -6)

Multiple Choice

What is the coordinate of the turning point of this quadratic $y=x^2+12x+6$  ?

• (-6, -30)

• (12, 6)

• (6, -30)

• (-12, 6)

Multiple Choice

What is the coordinate of the turning point of this quadratic $y=x^2-10x+6$  ?

• (-10, 6)

• (5, -19)

• (-5, -19)

• (10, 6)

Mathswatch

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