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

1. Jul 7, 2012

### duggielanger

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.

Last edited: Jul 7, 2012
2. Jul 7, 2012

### sjb-2812

Sounds a good place to me. What do you then get? Have you learnt e.g. completing the square, or the quadratic formula yet?

3. Jul 7, 2012

### duggielanger

Not answered the question yet ,and not done them yet they are coming up in the section.
Will try and find the answer in a bit and post my results .

4. Jul 7, 2012

### e^(i Pi)+1=0

Hint: since one side of the equation=0, you can easily multiply both sides by 5, and then -1...

5. Jul 7, 2012

### Curious3141

Note that you've dropped the minus sign on the coefficient of the $x^2$ term the last time you wrote that (in bold). That minus sign is all-important. Without that, you don't have an x-intercept!

6. Jul 7, 2012

### duggielanger

yeah thank you for that i will remember the minus sign

7. Jul 7, 2012

### HallsofIvy

Staff Emeritus
Once you have done what e^pi i + 1= 0 suggested, multiplying the entire equation by -5, you will have a quadratic equation with integer coefficients that is easy to factor.

8. Jul 7, 2012

### duggielanger

Ah right think I have it now , multiply by the least common denominator, which is 5, which leaves me with -x^2+x-30=0 and the by -1 to get x^2-x-30=0 and then factor to get (x+5)(x-6).
Thank you everyone

9. Jul 7, 2012

### HallsofIvy

Staff Emeritus
No, you get -x^2+ x+ 30 but then your next is correct:
Yes, that is correct.