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# Solving Quadratics: Choosing the Best Method

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Tweet## Benjamin Carter

on 15 April 2010#### Transcript of Solving Quadratics: Choosing the Best Method

SOLVING QUADRATICS Completing the Square Quadratic Formula Factoring Graphing / Finding

Zeros Find the magic number by taking half of b and squaring the result Make sure the equation is in the form x^2 + bx = c

Add the magic number to both sides

and then factor the perfect square

trinomial Factor the trinomial and then

set each factor equal to zero

and solve. Graph the equation manually or with your

graphing calculator.

Manually, plug points in for "x" and solve

for "y". You create 5-6 ordered pairs and

then you can plot them on a graph and connect

the points

Graphing calculator, plug equation in to the y=

and hit graph. You can use the trace button to

find your zeros.

Zeros, where the y is equal to zero / where the

graph crosses the x-axis. You either have two

zeros or no zeros at all.

The quadratic formula is a failsafe way

to solve quadratic equations. Which means,

it will always work. That does not mean that it is always the best or easiest method 1) Label a, b, and c

2) Plug into your quadratic formula

3) Simplify as much as possible (x-2)(x+4)=0 x - 2 = 0

x + 4 = 0 x = {2,-4} Here is an example how we would solve a quadratic equation using the quadratic formula. y = x² − 2x + 1

a =1

b = − 2

c = 1 1) x² - 7x 8 = 0 5x²-2x-1 = 0 {-1 , 8} 2) 2x² + 3x 9 = 0 3) {-3 , 3/2} x^2 - 6x + 2 = 0 x^2 - 14x - 44 = 0 x^2 + 2x - 5 = 0 Find the zeros of the following functions.

1) (x-2)(x+3)=0

2) (2x-5)(x+4)=0

3) (3x+2)(x-1)=0

Full transcriptZeros Find the magic number by taking half of b and squaring the result Make sure the equation is in the form x^2 + bx = c

Add the magic number to both sides

and then factor the perfect square

trinomial Factor the trinomial and then

set each factor equal to zero

and solve. Graph the equation manually or with your

graphing calculator.

Manually, plug points in for "x" and solve

for "y". You create 5-6 ordered pairs and

then you can plot them on a graph and connect

the points

Graphing calculator, plug equation in to the y=

and hit graph. You can use the trace button to

find your zeros.

Zeros, where the y is equal to zero / where the

graph crosses the x-axis. You either have two

zeros or no zeros at all.

The quadratic formula is a failsafe way

to solve quadratic equations. Which means,

it will always work. That does not mean that it is always the best or easiest method 1) Label a, b, and c

2) Plug into your quadratic formula

3) Simplify as much as possible (x-2)(x+4)=0 x - 2 = 0

x + 4 = 0 x = {2,-4} Here is an example how we would solve a quadratic equation using the quadratic formula. y = x² − 2x + 1

a =1

b = − 2

c = 1 1) x² - 7x 8 = 0 5x²-2x-1 = 0 {-1 , 8} 2) 2x² + 3x 9 = 0 3) {-3 , 3/2} x^2 - 6x + 2 = 0 x^2 - 14x - 44 = 0 x^2 + 2x - 5 = 0 Find the zeros of the following functions.

1) (x-2)(x+3)=0

2) (2x-5)(x+4)=0

3) (3x+2)(x-1)=0