Quadratics X-intercept Form (Algebra One)

After our initial investigations of Quadratic functions in general we start to look at the different forms of quadratic functions. We start with x-intercept form. This will pull in the factoring skill from the algebra skills mini-unit we just did.

Here is my lesson plan (which really ended up taking two class blocks)

Objectives

Students will be able to

• ·         Find the key features of a quadratic function when the function equation is in intercept form.
• ·        Convert standard form to intercept form and then proceed to determine key features.

Learning activities

·         Warm up – rocket problem. Students brainstorm together to answer questions about the rocket.

·         Let’s look more closely at graphs and key features of some quadratic function equations. WS “Explore Quadratic Functions” – students fill in table of values, graph & identify key features. They also factor and see if they notice anything about their factors and any of the characteristics. Should come to conclusion that the factors help us find the x-intercepts.

·         Let’s examine a few other function equations to see if we can come up with some rules to find key features using the equation, not the graph.

o   y = x² – 6x + 5  do together – what can we do to find key features? (factor – finds x-intercepts, discuss zero product property). How can we find the vertex? (give students some time to brainstorm without using graphing function of calculator - remember the property of symmetry. After a few minutes let them use graphing calculator graphs if necessary).

o   y = x² + 2x – 3

o   y = x² – 16

o   y = 2x² + 20x + 48

o   y = -x² – 4x + 32

o   y = x² + 6x + 9

o   y = -3x² + 12x + 63

·         Go back to original rocket problem. Relate the questions to the key features. Factor the original equation to see how those features can be determined algebraically.

·         Wrap up discussion of “intercept form” of quadratic functions and finding key features. Use ISN foldable.

·         Exit slip y = x² + 8x + 12 find x-intercepts, vertex, AOS, y-intercept and tell whether it opens up or down. Draw a rough sketch of the graph with parts labeled.

·         If time – do another application problem

o   The weekly profit function in dollars of a small business that produces fruit jams is

P(x) = 0.4x² + 40x + 360

where x is the number of jars of jam produced and sold.

a)      The small business “breaks even” when the profit is zero (cost & income are the same).  Determine at which point the business will break even (how many jars of jam produced & sold)

b)       Find the number of jars of jam that should be produced to maximize the weekly profit

c)       Find the maximum profit

·         Worksheet to start in class and finish for HW.

Here are my ISN pages

And this folder has all my ISN templates for this unit (8 blog posts worth! I'll post this link on each blog). It's way easier to upload them all together.

Here are supportingmaterials I used for this topic.