# Finding which graph represents the roots of an equation

#### Mariolee

Please explain thoroughly how to solve this! I do not understand how to do this.

42 Which graph best represents an equation that has the roots x= -7/2 and x=1/2?

F

G

H

J

#### Ackbeet

MHF Hall of Honor
So, in order to solve this, you have to understand what a root is. You tell me: what is a root?

mr fantastic

#### Mariolee

So, in order to solve this, you have to understand what a root is. You tell me: what is a root?
My understanding of a root was that it was a number or fraction that when plugged in for something like x or y, would satisfy the equation such as y=mx+b right?

#### Ackbeet

MHF Hall of Honor
Right. In this context, the equation that must be satisfied is $$\displaystyle y=f(x)=0.$$ What does this look like on a graph?

mr fantastic

#### Mariolee

Right. In this context, the equation that must be satisfied is $$\displaystyle y=f(x)=0.$$ What does this look like on a graph?
Wait, what does $$\displaystyle y=f(x)=0.$$ look like on a graph, or what do the roots x= -7/2 and x=1/2. If you mean the former, doesn't a function usually appear as a parabola, like in the answers above?

#### Ackbeet

MHF Hall of Honor
Let's say you have a function, call it $$\displaystyle y=f(x)$$. This is any ol' function, not necessarily a parabola. Could be a straight line, could be a parabola, could be a sine wave, etc. Let's say it has a "root" at $$\displaystyle x=3.$$ Graphically, what is happening to $$\displaystyle f(x)$$ at $$\displaystyle x=3$$?

mr fantastic

#### Mariolee

Let's say you have a function, call it $$\displaystyle y=f(x)$$. This is any ol' function, not necessarily a parabola. Could be a straight line, could be a parabola, could be a sine wave, etc. Let's say it has a "root" at $$\displaystyle x=3.$$ Graphically, what is happening to $$\displaystyle f(x)$$ at $$\displaystyle x=3$$?
To be honest, I'm teaching myself about all this function stuff, so please be patient with me.
Graphically, that means a line would be going straight through (3,0) if I understand the question correctly.

#### Ackbeet

MHF Hall of Honor
Correct! Or, well, you can say that the function goes through that point. It might not be going straight through that point.

So, going through the point (3,0) means that it is hitting an axis: is it the x or the y axis?

mr fantastic

#### Mariolee

Correct! Or, well, you can say that the function goes through that point. It might not be going straight through that point.

So, going through the point (3,0) means that it is hitting an axis: is it the x or the y axis?
X obviously.

#### Ackbeet

MHF Hall of Honor
Right. So, of the answers F, G, H, and J in the OP, which function hits the x axis at the points x = -7/2 and x = 1/2?