IGCSE Quadratic Equations and Graphs

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Mathematics

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10th Grade

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Practice Problem

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Medium

Fiona Davidson

Used 18+ times

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10 Slides • 40 Questions

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

Type response here

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

-8

-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)

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IGCSE Quadratic Equations and Graphs

Solve Quadratics

Identify features of Quadratic Graphs from the equation

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