Solving Quadratic Equations

By: Jessica Campos

Solving Quadratic Equations by Graphing

F(x)= x2-8x+15=0 X=(x-3)(x-5) X=3 and 5

Steps to put into a graph:◦ Enter equations into "Y =" area.  (Be sure the PLOTS at the top of window

are turned off.)  When the = sign is highlighted, the graph will be displayed.

◦ Choose the viewing window.◦ Hit GRAPH to see your graphs. If you need to find the roots of the

equation (the x-intercepts) you may choose #2 ZERO from the CALCULATE menu under CALC (above the TRACE key).

◦ If you need to see values relating to the graph, go to the TABLE (2nd GRAPH).  You can control what you see in the table by going to TBLSET (2nd WINDOW).

Solving Quadratic Equations byFactoring

o You must always have a zero product property. a=0 or b=0

• x2+21=10x• x2-10x+21=0• Factor: (x-7)(x-3)=0• x-7=0 and x-3=0• x=7 and x=3

1.) x2+4x-21=02.)x2+4x=213.)4/2=2 22=44.)(x+2)2=255.)√(x+2)2=√256.)x+2= +or- 25X= -27 X=23

Solving Quadratic Equations by using the Quadratic Formula

General Formula: x=-b+or-√b2-4ac

2(a)

2x2+12x-174=0122-4(2)(-174)= 1536x=-12+or-√1536

2(2)

X= 6.79 and X=-12.79

Which way is best?? I personally feel like the best way to solve

quadratic equations are by using the quadratic formula which is: x=-b+or-√b2-4ac

2(a) Keep in mind that using completeing the

formula is the only other method that will always give you a final correct answer while graphing and factoring may not always do so.