Solving Quadratic Equations using the Quadratic Formula

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Contributors

Hannah Bartholomew

History

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Hannah Bartholomew 8 years, 5 months ago

Created this as a copy of Solving Quadratic Equations using the Quadratic Formula and a Calculator.

Name	Status	Author	Last Modified
Factorising Quadratics 1 - Basic	Ready to use	Katie Lester	01/06/2016 09:47
Factorising Quadratics 2 - Intermediate	Ready to use	Katie Lester	01/06/2016 09:47
Factorising Quadratics 3 - Challenging	Ready to use	Katie Lester	01/06/2016 09:47
Factorising Quadratics 4 - Solving by Factorising or Using Formula	Ready to use	Katie Lester	01/06/2016 09:47
Factoring 2 Quadratics 2 of form: $ax^2+bx+c$	draft	Clare Lundon	05/10/2016 22:45
Factorising Quadratics 1: $x^2+bx+c$ 3 questions READY	draft	Clare Lundon	05/10/2016 22:46
steve's copy of Factoring Quadratics 2 $ax^2+bx+c$ 4 questions READY	draft	steve kilgallon	18/07/2016 16:05
Lucy's copy of Factoring Quadratics 2 $ax^2+bx+c$ 4 questions READY	draft	Lucy Hadfield	03/08/2016 10:50
Francis 's copy of Solving Quadratic Equations using the Quadratic Formula 4 Questions READY	draft	Francis Duah	12/08/2016 17:56
Gareth's copy of Lucy's copy of Factoring Quadratics 2 $ax^2+bx+c$ 4 questions READY	draft	Gareth Woods	26/08/2016 11:21
Kjell's copy of Francis 's copy of Solving Quadratic Equations using the Quadratic Formula 4 Questions READY	draft	Kjell Hansen	05/09/2016 11:01
Kjell's copy of Kjell's copy of Francis 's copy of Solving Quadratic Equations using the Quadratic Formula 4 Questions READY	draft	Kjell Hansen	05/09/2016 11:02
Solving Quadratic Equations using the Quadratic Formula and a Calculator	draft	Francis Duah	14/09/2016 16:55
Francis 's copy of Solving Quadratic Equations using the Quadratic Formula 4 Questions READY	draft	Francis Duah	14/09/2016 16:50
Factoring 1 Quadratic of form: $ax^2+bx+c$	draft	Clare Lundon	13/10/2016 10:06
Solving Quadratic Equations using the Quadratic Formula	draft	Hannah Bartholomew	18/09/2017 11:52
Ugur's copy of Factorising Quadratics 2 - Intermediate	Ready to use	Ugur Efem	01/11/2021 12:31
Ugur's copy of Factorising Quadratics 1 - Basic	Ready to use	Ugur Efem	04/11/2021 15:33

There are 19 other versions that do you not have access to.

Question statement

Solve the following quadratic equations with the quadratic formula: $x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	list	[ 2, 5, 2, 4 ]
b	list	[ -5, 5, 2, -8 ]
c	list	[ -6, -12, 0, -2 ]
disc1	number	73
disc2	number	265
disc3	number	4
disc4	number	96
ansmin	number	-0.8860
ansplus	number	3.386

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(1..5),4)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 2, 5, 2, 4 ]

→ Used by:

ansmin
ansplus
disc1
disc2
disc3
disc4

Advice
"Part a)" - prompt
"Part a)" → "Gap 0." - Minimum accepted value
"Part a)" → "Gap 0." - Maximum accepted value
"Part a)" → "Gap 1." - Minimum accepted value
"Part a)" → "Gap 1." - Maximum accepted value
"Part b)" - prompt
"Part b)" → "Gap 0." - Minimum accepted value
"Part b)" → "Gap 0." - Maximum accepted value
"Part b)" → "Gap 1." - Minimum accepted value
"Part b)" → "Gap 1." - Maximum accepted value
"Part c)" - prompt
"Part c)" → "Gap 0." - Minimum accepted value
"Part c)" → "Gap 0." - Maximum accepted value
"Part c)" → "Gap 1." - Minimum accepted value
"Part c)" → "Gap 1." - Maximum accepted value
"Part d)" - prompt
"Part d)" → "Gap 0." - Minimum accepted value
"Part d)" → "Gap 0." - Maximum accepted value
"Part d)" → "Gap 1." - Minimum accepted value
"Part d)" → "Gap 1." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part c) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part d) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Find the values of $x$ that solve the equation $\simplify{{a[0]}*x^2+{b[0]}*x+{c[0]}}=0$.

Give your answers in ascending order (ie smallest first) to four significant figures.

$x=$ Gap 0. and $x=$ Gap 1.

Advice

Worked example using Part a:

Find the roots of $\simplify{{a[0]}*x^2+{b[0]}*x+{c[0]}}=0$.

The quadratic formula is given by $x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

To solve this, simply input the numbers from the equation into the formula, defining the coefficient of $x^2$ as $a$, the coefficient of $x$ as $b$, and the constant as $c$.

Here, $x=$ $-(\var{b[0]})$$\pm$$\sqrt{(\var{b[0]})^2-4(\var{a[0]}\times\var{c[0]})}$$2\times\var{a[0]}$

Inputting these figures into a calculator, starting with the minus sign before the root, gives: $x=\var{ansmin}$,

and using the positive root version gives the other solution: $x=\var{ansplus}$.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Quadratic Formula by Gareth Woods in Gareth's workspace.
Test 3 - functions and graphs by Hannah Bartholomew in Hannah's workspace.

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Error

Solving Quadratic Equations using the Quadratic Formula

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Hannah Bartholomew 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

Loading...

Error

Solving Quadratic Equations using the Quadratic Formula

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Hannah Bartholomew 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`