Graphing Simple Quadraticsy = ax2 + c

Objective: Students will graph simple quadratic functions

Graph the Parent Functiony = x2

1) Make an x-y table2) Pick any values for x3) Solve for y for each

x4) Place ordered pairs

on the graphx y

-2-1012

41014

Graph y = 3x2 and Compare your results with the Parent Function

1) Make an x-y table2) Pick any values for x3) Solve for y for each

x4) Place ordered pairs

on the graphx y

-2-1012

1230312

When a > 1 the graph is narrower

Graph y = -1/4x2 and Compare your results with the Parent Function

1) Make an x-y table2) Pick any values for x3) Solve for y for each

x4) Place ordered pairs

on the graphx y

-4-2024

-4-10-1-4 Because a is negative the graph is reflected and

when a < 1 then the graph is wider

Graph y = x2 + 5 and Compare your results with the Parent Function

1) Make an x-y table2) Pick any values for x3) Solve for y for each

x4) Place ordered pairs

on the graphx y

-2-1012

96569

When a value is added (or subtracted) to x2 the graph moves up (or down) but is the same graph as the parent function

Match the Quadratic Function with its Graph

1. Y = x2 - 4 2. Y = -x2 + 4 3. Y = 4x2 – 44. Y = ¼ x2 - 4

C

A B

D E

• Write at least one sentence to describe difference between the given function and the Parent Function y = x2

1) Y = 7x2

2) Y = -x2

3) Y =x2 – 7 4) Y = 1/2x2

5) Y = 1/5x2 + 2

• Sailors need to consider the speed of the wind when adjusting sails on their boat. The force f (in pounds per square foot) on a sail when the wind is blowing perpendicular to the sail can be modeled by the function f = 0.004v2 where v is the wind speed ( in knots).

a) Graph the function for wind speed from 0 to 50 knots.b) Use the graph to estimate the wind speed that will

produce force of 1 pound per square foot on a sail.c) Estimate the wind speed that will produce a force of 5

pounds per square foot.

In the Giant Redwood forest a pinecone falls about 144 feet from the branch of a pine tree. Its height (in feet) can be modeled by the function h(t) = -16t2 + 144, where t is the time in seconds.

a) Graph the function.b) At what height is the

pinecone at 1 second.c) At what height is the

pinecone at 2 seconds.d) After how many seconds

does the pinecone hit the ground