The document provides information about solving quadratic equations using the quadratic formula. It defines the quadratic formula and shows how to use it to solve quadratic equations in standard form. It also discusses using the discriminant to determine the number of real solutions a quadratic equation will have. An example problem demonstrates using the quadratic formula to solve a word problem about profit from wrapping paper sales.

1. 4-7 THE QUADRATIC FORMULA
Chapter 4 Quadratic Functions and Equations
©Tentinger

2. ESSENTIAL UNDERSTANDING AND
OBJECTIVES
 Essential Understanding: you can solve quadratic
equations in more than one way. In general you can
find a formula that gives the values of x in terms of
a, b, and c
 Objectives:
 Students will be able to:
 Solve quadratic equations using the quadratic formula
 Determine the number of solutions using the discriminant

3. IOWA CORE CURRICULUM
 Algebra
 Reviews A.REI.4b. Solve quadratic equations in
one variable.
 Solve quadratic equations by inspection taking square
roots, completing the square, the quadratic formula and
factoring, as appropriate tot eh initial form of the
equation. Recognize then the quadratic formula gives
complex solutions and write them as
a±bi for real numbers a and b.

4. DERIVE THE QUADRATIC FORMULA
 Use the quadratic formula to solve equations in
standard form. If the equation is not in standard
form, use algebra to put the equation into standard
form

5. USING THE QUADRATIC EQUATION
 What are the solutions to the following equations?
 2x2 – x = 4
 x2 + 4x = -4
 x2 + 4x – 3
 5x2 – 2x = 2

6. EXAMPLE
 You sell wrapping paper as a charity fundraiser.
The equation p = -6x2 + 280x -1200 models the
total profit p as a function of the price x per roll of
paper. What is the smallest amount in dollars you
can charge per roll of wrapping paper to make a
profit of $1500?

7.  Solutions to Quadratics
 Two real solutions, one real solution, or not real solutions
 Discriminant: the value of b2 – 4ac
 This tells you how many real solutions an equation has.
 If b2 – 4ac > 0 there are two real solutions. What does this
graph look like?
 If b2 – 4ac = 0 there is one real solution. What does this graph
look like?
 If b2 – 4ac < 0 there is no real solution. What would this graph
look like?

8.  What is the number of real solutions to the
equations:
 -2x2 – 3x + 5 = 0?
 2x2 – 3x + 7
 x2 = 6x + 5
 -x2 + 14x = 49

9. EXAMPLE
 A rocket is launched from the ground with an initial
vertical velocity of 150 ft/s. The function
h = -16t2 + 150t models the height in feet of the
rocket at time t in seconds. Will the rocket reach a
height of 300 ft? Explain your answer.

10. HOMEWORK
 Pg. 245 – 246
 # 12 – 21 (3s), 23, 24, 26 – 39 (3s), 46 – 49, 70
 16 problems