1. ALGEBRA II HONORS/GIFTED - SECTION 4-7 (The Quadratic Formula)@
SECTION 4-7 : THE QUADRATIC FORMULA

2. Solve using the quadratic formula.
3x2 + 5x + 1 = 0
a = 3, b = 5, c = 1

3. Solve using the quadratic formula
Solve using the quadratic formula. Do the problem associated with your group number.
ANSWERS
2x2 – 20x – 30 = 0
x2 + 2x + 8 = 0
x2 – 12x – 24 = 0
x2 – 4x + 4 = 0
9x2 + 30x + 25 = 0
5x2 + 30x + 65 = 0
x2 – 13x + 40 = 0
x2 – 6x + 7 = 0 2
5, 8
Just for fun, find the value of the discriminant – b2-4ac – for each of the problems.

4. ALGEBRA II HONORS/GIFTED - SECTION 4-7 (The Quadratic Formula)
According to the Discriminant Test we can determine the nature
of the roots.
If b2-4ac is a perfect square, you get 2
Rational roots. If not, you get 2 Irrational
roots.
Determine the nature of the roots.
9) 2x2 + 9x – 6 = 0
11) 4x2 – 28x + 49 = 0
10) 6x2 – 2x + 7 = 0
12) x2 + 12x + 32 = 0

5. Time for a little work with your
13) We know 2x2 – 20x – 30 = 0 has two real zeros. Graph the polynomial.
a) Using the graph, how do you know the polynomial has two real zeros?
b) Is there another way a parabola can be positioned to show two real zeros?

6. 14) We know that x2 – 4x + 4 = 0 has one real zero
14) We know that x2 – 4x + 4 = 0 has one real zero. Graph the polynomial.
a) How can you tell by looking at the graph there is exactly one real zero?
b) Is there another way the parabola can be positioned to give you one real zero?

7. 15) We know the polynomial x2 + 2x + 8 = 0 has no real zeros
15) We know the polynomial x2 + 2x + 8 = 0 has no real zeros. Graph the polynomial.
a) How can you tell by looking at the graph there are no real zeros?
b) Is there another way the parabola can be positioned giving no real zeros?

8. 16) Kinsey is selling gift wrapping paper for a charity fundraiser
16) Kinsey is selling gift wrapping paper for a charity fundraiser. The equation p = -6x x – models the total profit, p, as a function of x, the price of each roll. What is the smallest amount of money Kinsey can charge per roll of wrapping paper to make a profit of $1500?
ANSWER : $13.62

9. Noah, the rocket scientist, launched a rocket
from the ground with an initial vertical velocity of 150 m/s. The flight of the rocket can be modeled by the equation h = -16t t giving the height in meters of the rocket after t seconds. Will Noah’ rocket ever reach a height of 300 meters? Explain your answer.
ANSWER : Yes. If you look at the table on your graphing calculator, the rocket is above 300 meters between 3 and 6 seconds.