Question

Use complete sentences to explain how you would use graphing technology to find the solutions of 0 = 2x2 − 3x + 0.5. What do the solutions of 0 = 2x2 − 3x + 0.5 represent on the graph of the equation?

Answer 1

do you mean 2x^2-3x+0.5

Answer 2

yes

Answer 3

how would you graph this by hand?

Answer 4

Im not quite too sure I'm having trouble with this part of algebra

Answer 5

you would just plug in points right? for example, plug in x=2, then y= ?

Answer 6

just like any other equation?

Answer 7

exactly. a computer does the same thing, except it plugs in a whole lot of different points for you.

Answer 8

Ok, but how would I use "Graphing Technology"

Answer 9

well, what does it mean to get a solution to something like x^2+2x+1=0?

Answer 10

To find the parabola?

Answer 11

right. so when I use the quadratic equation to find the "solution" I'm asking where does this function equal zero

Answer 12

in other words, at what point will this function cross the x-axis

Answer 13

But what if it doesn't?

Answer 14

good question! then you don't have any real solutions. For this problem, it looks like this: http://www.wolframalpha.com/input/?i=+2x^2+%E2%88%92+3x+%2B+0.5

Answer 15

Ok that makes sense. But how would i solve to get where it does or doesn't cross?

Answer 16

you have to use the quadratic equation. this is essentially what the "graphing technology" does to give you the solutions. It looks for the points on the x axis where y=0. so for a parabola you will sometimes have two points that look like this (a,0) and (b,0)

Answer 17

So those points would mean where the parabola intercepts the x axis, and I don't need this "graphing technology" I can just solve it?

Answer 18

Exactly, it is the intercepts. Sometimes it is easier to use a graphing technology though because it is very fast at plotting the points and doing the quadratic equation