# Use algebra to find the x and y intercepts , for a quadratic equation

• July 7th 2012, 01:41 AM
duggielanger
Use algebra to find the x and y intercepts , for a quadratic equation
1. The problem statement, all variables and given/known data

Use algebra to ﬁnd the x-intercepts and y-intercept of The graph of y=-x^2/5+x/5+6
this is a parabola.

2. Relevant equations
y=-x^2/5+x/5+6

3. The attempt at a solution
Find the y-intercept , which is substitute 0=x into the equation to find the answer , done that .
The problem I have is where to start to find the x-intercept , I know that y=0 so I now have x^2/5+x/5+6=0 , but believe I can't now factorise this equation and will have to first clear the fractions first . Is this the right place to start.
• July 7th 2012, 01:50 AM
johnnylam123
Re: Use algebra to find the x and y intercepts , for a quadratic equation
is it y=-x^2/5+x/5+6 or x^2/5+x/5+6=0?,
btw, for -x^2/5+x/5+6=0, then x^2-x-30=0, x = (1+/- 11)/2, ie x=6 or -5
• July 7th 2012, 01:53 AM
biffboy
Re: Use algebra to find the x and y intercepts , for a quadratic equation
Sorry missed the - sign in front of x^2 in my first reply. Method of course still applies.
• July 7th 2012, 02:49 AM
duggielanger
Re: Use algebra to find the x and y intercepts , for a quadratic equation
The equation is y=-x^2/5+x/5+6 and I'm looking for the x-intercept .
• July 7th 2012, 04:40 AM
Plato
Re: Use algebra to find the x and y intercepts , for a quadratic equation
Quote:

Originally Posted by duggielanger
The equation is y=-x^2/5+x/5+6 and I'm looking for the x-intercept .

Can you solve $x^2-x-30=0~?$ That is all that is needed.
• July 7th 2012, 06:56 AM
duggielanger
Re: Use algebra to find the x and y intercepts , for a quadratic equation
I think I can , I would factorise this equation to get my final answer. which is (x-1)(x+5) I think, and these are my x-intercepts. But to get this part do I simply the fraction by finding the the products of 5 and 6 and then simplify to x^2-x-30=0.
And sorry one last question, would squaring and or using then quadratic formula get the same answer.
• July 7th 2012, 07:08 AM
Plato
Re: Use algebra to find the x and y intercepts , for a quadratic equation
Quote:

Originally Posted by duggielanger
I think I can , I would factorise this equation to get my final answer. which is (x-1)(x+5) I think, and these are my x-intercepts. But to get this part do I simply the fraction by finding the the products of 5 and 6 and then simplify to x^2-x-30=0.
And sorry one last question, would squaring and or using then quadratic formula get the same answer.

It factors as $(x-6)(x+5)$. Thus your x-intercepts are $(6,0)~\&~(-5,0)($
• July 7th 2012, 07:31 AM
duggielanger
Re: Use algebra to find the x and y intercepts , for a quadratic equation
Ok thank you , I will go back and study the section again to get to grips with it.