Solve Quadratic Equations by the Quadratic Formula
Goals • Solve quadratic equations using the
Quadratic formula A formula that gives the solutions
of any quadratic equation in standard form
|THE QUADRATIC FORMULA
The roots of the polynomial and the
solutions of the quadratic equation
|Example 1 Multiple Choice Practice|
|Which is one of the solutions to the
in the quadratic
formula: a = 2 ,
b = -3 , and
c = -5 .
|One solution is -1. The correct
answer is B
|Your Notes||Example 2 Use the quadratic formula|
|Crabbing A crabbing net is thrown
from a bridge, which
is 35 feet above the water. If the net's initial velocity is
10 feet per second, how long will it take the net to hit
The net's initial velocity is v = 10 feet per second and
the net's initial height is s = 35 feet. The net will hit
the water when the height is 0 feet.
|Vertical motion model|
|Substitute for h, v, and s.|
in the quadratic
a = -16 ,
b= 10 , and
c = 35 .
|The solutions are and|
cannot be a
| So, the net
will hit the water
in about 1.82 seconds.
|Guided Practice Complete the following exercises.|
|1. Use the quadratic formula to solve
|2. In Example 2, suppose the net was
thrown with an
initial velocity of 5 feet per second from a height of
20 feet. How long would it take the net to hit the
about 1.29 seconds
|Your Notes||METHODS FOR SOLVING QUADRATIC EQUATIONS|
|Methods||When to Use|
|Factoring||Use when a quadratic equation can be
|Graphing||Use when approximate solutions are
|Finding||Use when solving an equation that can|
|square roots||be written in the form x2 = d .|
|Completing||Can be used for any quadratic equation|
|the square||Can be used for any quadratic equation
the square but is simplest to apply
when a = 1 and b is an even number.
|Quadratic||Can be used for any quadratic equation.|
|Example 3 Choose a solution method|
|Tell what method(s) you would use to
quadratic equation. Explain your choice(s).
a. The quadratic equation cannot be factored easily
and completing the square would result in many
fractions . So, the equation can be solved using
the quadratic formula .
b. The quadratic equation can be solved using square
roots because the equation can be written in the
form x2 = d.
|Guided Practice Complete the following exercise.|
|Homework||3. Tell what method(s) you would use
. Explain your choices(s).
factoring: the expression can be factored easily;
completing the square: the equation is of the
form where a= 1 and b is an