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Solving Quadratics: Choosing the Best Method

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Benjamin Carter

on 15 April 2010

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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





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