National 5
Name: _________________
1. We equate a quadratic
function to 0 when we want to
find where the parabola goes
through the x – axis (the roots)
y = 0.
3. What happens if we
cannot factorise a
quadratic equation…
E.g. x2 + 2x + 2
Quadratic
Equations
2. The easiest way to solve a
quadratic equation is to
factorise it first.
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This type of equation
doesn’t have roots that
are integers. We
therefore must use a
formula to find the roots.
The Quadratic Formula:
When y = ax2 + bx + c
For
Example:
State
theour
roots
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of Ifthe
quadratic
function
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y = x2 + 2x - 8
FX Equation 4. Otherwise contact Efofex Software or one of our agents to purchase a
=> y = (x - 2)(x + 4)
=> subscription.
0 = (x – 2)(x + 4)
4. Example: Find the roots of x2 + 3x - 7
a=1
b = 3 c = -7
When two variables multiply
to get zero, at least one must
x = -3 ± √32 – 4(1)(-7)
= -3 ± √37
be equal to zero
2(1)
2
 x – 2 = 0 or x + 4 = 0
 x=2
or
x = -4
=> x = 1.54 or x = -4.54
5. The discriminant of a quadratic equation
determines the type of roots a quadratic has.
i.e. the graph cuts the x – axis at (1.54, 0)
and (-4.54, 0)
It is found by calculating b2 – 4ac
when y = ax2 + bx + c
If b2 – 4ac < 0 => Roots cannot be found*
If b2 – 4ac > 0 => Two distinct real roots
If b2 – 4ac = 0 => There is 1 real root
Name: ____________________
This unit, I would like to find out more about:
________________________________________________________________________
________________________________________________________________________
*roots can be found but are complex numbers, you will study this in Advanced Higher!
National 5
Unit 2 – Relationships: Outcome 1 (1.3) Quadratic Equations
What do I need to know?
I can recognise a quadratic function given its equation.
I can factorise a quadratic function.
I understand that y = 0 when the parabola cuts the x – axis.
I understand that if two variables multiply to get zero, then at least one must be
equal to zero.
I can find the roots of a quadratic function by factorising it, equating to zero and
finding the value(s) of x.
If I cannot find factors for a quadratic function, I know that I must use the
quadratic formula.
I am familiar with the quadratic formula and am able to work out the roots of a
quadratic function by substituting in my values for a, b and c when
y = ax2 + bx + c
I understand what is meant by the discriminant (b2 – 4ac) of a quadratic
function.
I know that if b2 – 4ac > 0, then there are two distinct real roots.
I know that if b2 – 4ac = 0, then there is 1 repeated root.
I know that if b2 – 4ac < 0, then I will not be able to find the roots.
Homework
I have completed the homework issued for this unit Yes/No
If not, why not?
What I need to work on for future homework is …
Notes/Comments to help me remember/revise:
National 5
Unit 2 – Relationships: Outcome 1 (1.3) Quadratic Equations