4.10: Write Quadratic Functions and Models

4.10: Write Quadratic Functions and Models
Objectives:
1. To write a quadratic
function given a
graph or collection of
points
Assignment:
• P. 312-315: 1, 2, 3-45
M3, 48, 49, 53-54
• Begin your search for
digital images of
parabolas (IRL)
Objective 1
You will be able to write a
quadratic function given a graph
or a collection of points
𝒚 = −𝟎. 𝟏𝟏𝒙𝟐 + 𝟐. 𝟒𝟒𝒙 − 𝟐. 𝟗𝟔
Vocabulary
Line of Best Fit
Quadratic Regression
Linear Regression
Exercise 1
Exactly how many
points does it
take to write the
equation of a
line?
Exercise 2
One for each parameter!
Exactly how many points does it take to write
the equation of a parabola?
y  a  x  h  k
2
y  a  x  p  x  q 
y  ax2  bx  c
Vertex Form
If you are given the
vertex and one
other point on the
parabola, you can
use the vertex form
of a quadratic
function to find its
equation.
y  a  x  h  k
2
Vertex Form
1. Plug in your vertex
values for h and k.
2. Plug in your
second point for x
and y.
3. Solve for a.
4. Write your
equation.
y  a  x  h  k
2
Exercise 3
Write the quadratic
function for the
parabola shown.
Exercise 4
Write a quadratic function whose graph has
the given characteristics.
1. Vertex: (4, -5)
Passes through: (2, -1)
2. Vertex: (-3, 1)
Passes through: (0, -8)
Intercept Form
If you are given the xintercepts and one
other point on the
parabola, you can
use the intercept
form of a quadratic
function to find its
equation.
y  a  x  p  x  q 
Intercept Form
1. Plug in your xintercept values for
p and q.
2. Plug in your 3rd
point for x and y.
3. Solve for a.
4. Write your
equation.
y  a  x  p  x  q 
Exercise 5
Write the quadratic
function for the
parabola shown.
Exercise 6
Write a quadratic function whose graph has
the given characteristics.
1. x-intercepts: -2, 5
Passes through: (6, 2)
2. x-intercepts: -4, 0
Passes through: (-3, -4.5)
Standard Form
If you are given any
three points on your
parabola, you can
use the standard
form of a quadratic
function to get the
equation.
y  ax  bx  c
2
Standard Form
1. Plug in 1st point for x
and y. Put in standard
form. This is Eq. 1.
2. Repeat Step 1 for 2nd
point. This is Eq. 2.
3. Repeat Step 1 for 3rd
point. This is Eq. 3.
y  ax  bx  c
2
Standard Form
4. Solve the system
formed from Eqs. 1, 2,
and 3 for a, b, and c.
5. Write your equation.
y  ax  bx  c
2
Exercise 7
Write the quadratic
function for the
parabola shown.
Exercise 8
Write a quadratic function in standard form
for the parabola that passes through the
given points
1. (-1, 0), (1, 2), (2, -15)
2. (-2, 30), (1, 6), (4, 36)
Quadratic Regression
Quadratic Regression is the process of
finding a best-fitting quadratic model for a
set of data. This is best done on a
calculator!
Quadratic Regression
Exercise 9
A pumpkin tossing contest is held each year in
Morton, Illinois, where people compete to see
whose catapult will send pumpkins the farthest.
One catapult launches pumpkins from 25 feet
above the ground at a speed of 125 feet per
second.
Exercise 9
The table shows the horizontal distance (in feet)
the pumpkins travel when launched at different
angles. Use a calculator to find the best-fitting
quadratic model for the data. At what angle
should the pumpkin travel the farthest?
Exercise 10
The drama club at your high school sells T-shirts
as a fundraiser. The table below shows data
from the last four years for the price charged for
a T-shirt, x, and the total revenue earned from
selling them, y. Use a calculator to find the bestfitting quadratic model for the data. What price
yields the highest revenue?
x
y
8
1180
10
1450
12
1675
14
1550
4.10: Write Quadratic Functions and Models
Objectives:
1. To write a quadratic
function given a
graph or collection of
points
Assignment
• P. 312-315: 1, 2, 345 M3, 48, 49, 5354
• Begin your search
for digital images of
parabolas (IRL)
“I like powabowas IRL!”