9.6 – Applications of the

Discriminant

Algebra 1(B)

Homework Check/Questions

44) ; -3, 545) ; 1, 246) ; 1.73, 9.2753) 4, -254) 4, -155) -2, 3

22 4 30 0x x

2 3 2 0x x 2 11 16 0x x

Warm UpUse the quadratic formula to solve the following problem:

Mr. V has just autographed a math textbook for the Biebs (aka Justin Bieber). Still in shock over who he has just met, Justin Bieber drops the book. A falcon flying overhead decides he would like to make some money by selling the book on Amazon. If the falcon is 100 feet in the air and dives at a speed of 220 feet per second, how much time does Justin Bieber have to react before the falcon takes the book?

Warm Up

I can’t believe that just happened. It was Mr. V! OMG!

Autographed Textbook

220 ft/sec

Answer: 0.44 sec

Objectives:

1. Evaluate the discriminant

2. Use the discriminant to find the number of quadratic solutions

3. Match graphs with their quadratic equations based on the discriminant

Recall the Quadratic Formula…

𝑥=−𝑏±√𝑏2−4𝑎𝑐2𝑎

Discriminant: the expression inside of the radical.

𝒃𝟐−𝟒𝒂𝒄

𝑏2−4𝑎𝑐

Using the Discriminant

Discriminant: the expression inside of the radical.𝑏2−4𝑎𝑐

PracticeDiscriminant: the expression inside of the radical.𝑏2−4𝑎𝑐

Use the discriminant to determine how many x-intercepts/solutions/zeros the following quadratic equations have.

one solution

no solution

two solutions

PracticeDiscriminant: the expression inside of the radical.𝑏2−4𝑎𝑐

Use the discriminant to determine how many x-intercepts/solutions/zeros the following quadratic equations have. Support your answer up by graphing!

𝑦=𝑥2−3𝑥−4

two solutions

PracticeDiscriminant: the expression inside of the radical.𝑏2−4𝑎𝑐

Use the discriminant to determine how many x-intercepts/solutions/zeros the following quadratic equations have. Support your answer up by graphing!

𝑦=2 𝑥2−2 𝑥+3

no solution

PracticeDiscriminant: the expression inside of the radical.𝑏2−4𝑎𝑐

Use the discriminant to determine how many x-intercepts/solutions/zeros the following quadratic equations have. Support your answer up by graphing!

𝑦=−𝑥2+2 𝑥−1

one solution

MatchingDiscriminant: the expression inside of the radical.𝑏2−4𝑎𝑐

Use the discriminant to match the equations with their potential graphs!

𝑦=𝑥2+2𝑥+2 𝑦=𝑥2−4 𝑥+4 𝑦=−3𝑥2+6 𝑥−1

A. B. C.

A C B

Exit Slip Raffle• Complete the three problems below.• Exit slips will be collected and random slips will be drawn.• If your paper is drawn and you are correct, you must explain your work for the class.• Prize: extra credit on tomorrow’s quiz!

Tell if the equation has two solutions, one solution, or no solution.

23 12 12 0x x

22 10 6 0x x

3) Is it possible for the equation below to have a graph like the one shown. EXPLAIN!

2 3 5 0x x1) 2)

One solution No solution

No, because the discriminant of the equation is positive, so the graph

should have two x-intercepts.

Assignment/Reminder

pg. 544 #9-17

Quiz 9.4-9.6 Monday 4/6!