MODELLING REPRESENTING Quadratic function

MODELING,
REPRESENTING
AND
TRANSFORMING
QUADRATIC
FUNCTIONS

HERE ARE SOME EXAMPLES OF SITUATIONS
THAT MODELS QUADRATIC FUNCTIONS IN
REAL-LIFE SITUATIONS.
1. Targets an object in upward direction
2. Throwing an object downward
3. Shooting ball vertically upward
4. Minimum point submarine to submerge
5. Launching rocket to its maximum point

Identify if the following are
QUADRATIC FUNCTION or NOT
Quadratic function since its
highest degree is 2 and all
numerical coefficients are
real numbers.
NOT quadratic function
since its highest degree is 1.
NOT quadratic function because if you will
expand the right side, its highest degree will be 4.

Observe the trend/characteristics
of the graph for you to determine
how quadratic function is.

How will you know if a table of values is
quadratic function? The test called second-
difference is used to determine whether a
table of values is quadratic or not. If there is a
common second difference, then the table is
quadratic. Study the example below:

Try this. Which of the following table of
values represent quadratic function.
QUADRATIC
FUNCTION
NOT QUADRATIC
FUNCTION

▪A quadratic function has a form
y = ax2
+ bx + c where a ≠ 0.
▪The graph of a quadratic function is
U-shaped and is called parabola.
PROPERTIES OF PARABOLA
▪Vertex.The lowest or highest point
on the graph of a quadratic function
▪Axis of symmetry.
▪Opening of the parabola
▪Intercepts
Axis of symmetry
x-intercepts
y-intercept
QUADRATIC FUNCTION
vertex
Opening of the
parabola

TRANSFORMING
QUADRATIC EQUATIONS
IN GENERAL FORM
TO STANDARD FORM

TRANSFORMING
QUADRATIC EQUATIONS
IN STANDARD FORM
TO GENERAL FORM

Multiply the perfect square
trinomial by 3
Simplify
Example
SOLUTION

Practice Exercises:
3. Rewrite
ANSWER: 𝑦=− ( 𝑥−3)2
+25

THE GRAPH OF A QUADRATIC
FUNCTION
vertex
Axis of
symmetry
y = x2
y = -x2
▪ The parabola opens up if and opens
down if .
▪ The parabola is wider than the graph of
if and narrower than the graph of if .
▪The x-coordinate of the vertex is
▪The y-coordinate of the vertex is
▪The axis of symmetry is the vertical line

EXAMPLE: Graph y = 2x2
-8x
+6
Solution: The coefficients for this function are
a = 2, b = -8, c = 6.
Since a>0, the parabola opens upward
The x-coordinate is: x = ; x = ; x = 2
The y-coordinate is: y =
y = ; y = -2
Hence, the vertex is (2,-2)

EXAMPLE(contd.)
▪Draw the vertex (2,-2) on graph.
▪Draw the axis of symmetry
▪Draw two points on one side of the
axis of symmetry such as (1,0) and
(0,6).
▪Use symmetry to plot two more
points such as (3,0), (4,6).
▪Draw parabola through the plotted
points.
(2,-2)
(1,0)
(0,6)
(3,0)
(4,6)
Axis of symmetry
x
y

GRAPHING A QUADRATIC FUNCTION
IN STANDARD FORM
Example
where a = -1/2, h = -3, k = 4.
Since a<0, the parabola opens down.
▪To graph a function, first plot the vertex
(h,k) = (-3,4).
▪Draw the axis of symmetry x = -3
▪Plot two points on one side of it, such as
(-1,2) and (1,-4).
▪Use the symmetry to complete the graph.
(-3,4)
(-7,-4)
(-1,2)
(-5,2)
(1,-4)
Axis of symmetry
x
y

MODELLING REPRESENTING Quadratic function

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