introduction to quadractics

Warm up: Perimeter card

1. Start notes on quadratics

2. Vocabulary investigation

3. Finish notes

4. Superhero quadractic

5. Exit Ticket

Goal: I can identify characteristics of quadratic functions

To find the dimensions :

Multiply your base by 2. Subtract that number by 40. Divide by 2 for dimension.

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Open Ended

What has parabolic motion or parabolic shape in the real world?

Quadratic Functions

When you throw a
ball (or shoot an

arrow, fire a missile
or throw a stone) it
goes up into the air,
slowing as it travels,

then comes down
again faster and

faster ...

​Find your partner: Look under your card and find your match :)

You will have 20 minutes to go through the vocabulary investigation worksheet. Everyone will need to fill out the packet.

What is a
quadratic
function?

All quadratic equations

are written in the

standard form

f(x) = a𝑥²+ b𝑥 + c

where a, b, and c are

numbers.

The graph of a quadratic
function is a curve called
a parabola. Parabolas may
open upward or downward

and vary in "width" or

"steepness", but they all
have the same basic "U"

shape.

Multiple Choice

Which of the following equations matches standard form of a quadratic?

• ax + by = c

• y = a(x - h)² + k

• y = ax² + bx + c

• y = mx + b

Parabola

The graph of a

quadratic

function is a
parabola, a u-
shaped figure.

The parabola will
open upward or

downward.

If ‘a’ is positive,
Then the parabola
opens up as a smile

☺

If ‘a’ is negative,

Then the parabola opens

down like a frown :(

Multiple Choice

What shape is the graph of a quadratic?

• Hyperbola

• Parabola

• Straight Line

• Circle

A ball is thrown
straight up from

3m above the
ground with a
velocity of 14

meters per second.

When does it hit

the ground?

H = 5t2+ 14t + 3

It shows you the height of the ball

vs time

Some interesting points:

(0,3) When t=0 (at the start) the

ball is at 3 m

(−0.2,0) says that −0.2 seconds

BEFORE we threw the ball it was at
ground level. This never happened!

So, our common sense says to

ignore it.

(3,0) says that at 3 seconds the

ball is at ground level.

Also notice that the ball

goes nearly 13 meters high.

Multiple Select

Parabolas can open which of the following ways?

• Up

• Down

• Right

• Left

Multiple Choice

Which letter determines if a parabola opens up or down?

• a

• h

• k

An axis of symmetry
(also known as a line

of symmetry) will
divide the parabola
into mirror images.

The line of symmetry

is always a vertical

line
𝑥 = 3

Axis of Symmetry

Multiple Choice

What is the green dashed line called?

• roots or x-intercepts

• parabola

• axis of symmetry

• line of dashes

Multiple Choice

What is the axis of symmetry for this graph?

• y=2

• x=2

• x=0

• y=0

Vertex

The point on the

parabola that
lies on the axis

of symmetry

(3, −4)

VERTEX

Multiple Choice

What is the vertex of this parabola?

• (0, 5)

• (2, 1)

• (-1, 2)

• (-2, 1)

Multiple Choice

The vertex of this quadratic is...

• (1,16)

• (-3,0)

• (5,0)

• (0,15)

Open Ended

Explain how the vertex and the axis of symmetry are related.

MINIMUM

A parabola that

opens upward

contains a

vertex that is a
minimum point.

MINIMUM

MAXIMUM

A parabola that
opens downward

contains a

vertex that is a

highest point

(−1, 2)

MAXIMUM

Multiple Choice

Does this graph have a maximum or minimum value?

• maximum

• minimum

• neither

• both

Multiple Choice

When the vertex is the lowest point on the graph, we call that a...

• Maximum

• Minimum

• Parabola

• Point of Interest

Multiple Choice

Does the graph have a minimum or a maximum?

• minimum

• maximum

Y-Intercepts

The point at which
a parabola crosses

the y-axis.

(0, −2)

X-Intercepts

The point(s) at
which a parabola
crosses the x-

axis.

(−1,0)(2,0)

X-INTERCEPTS

ZEROS

The x values

of the

x-intercepts.

−1 𝑎𝑛𝑑 2

ZEROS

Domain

All possible x values of a function

For parabolas the domain is all real numbers.

ZEROS

Range

All possible y values of a function

y can only be values less than or equal to 10 so the

Range is y ≤ 10

ZEROS

Poll

Which vocabulary word seems the most difficult to understand?

• Domain/Range

• Axis of symmetry

• Vertex

• Min/Max

• Zeros

A ball is thrown
straight up from

3m above the
ground with a
velocity of 14

meters per second.

When does it hit

the ground?

H = 5t2+ 14t + 3

It shows you the height of the ball

vs time

Some interesting points:

(0,3) When t=0 (at the start) the

ball is at 3 m

(−0.2,0) says that −0.2 seconds

BEFORE we threw the ball it was at
ground level. This never happened!

So, our common sense says to

ignore it.

(3,0) says that at 3 seconds the

ball is at ground level.

Also notice that the ball

goes nearly 13 meters high.

Sample Quadratic Problem

In the new hit Super Jump video game, you beat the final level by making your
character leap off a truck to catch his enemy. Your character follows the curve:
y = -2x2+4x+6 as he leaps to capture his nemesis.
Complete the table of values below to find his location at various points during
his jump.
Sketch your values and connect them as a curve.

X

Y

0

1

2

3

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​Fill in the worksheet with your elbow partner

Sample Problem: Reflections

(1,8) The maximum height reached was 8 feet after 1 second.

(6,0) The height of the truck was 6 feet.

(0,3) It took 3 seconds to reach the enemy (at ground level).

The first value represents the height above ground as he
jumps up and the second represents his height as he
comes back down.

© Limitless Lessons

Can’t have negative time (so no negative x) and the character
can’t go below ground (so no negative y)