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

[duggielanger]

Homework Statement

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.

Homework Equations

y=-x^2/5+x/5+6

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.

 

[sjb-2812]

Homework Statement

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.

Homework Equations

y=x^2/5+x/5+6

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.

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

 

[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 .

 

[e^(i Pi)+1=0]

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

 

[Curious3141]

Homework Statement

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.

Homework Equations

y=-x^2/5+x/5+6

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.

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!

 

[duggielanger]

yeah thank you for that i will remember the minus sign

 

[HallsofIvy]

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.

 

[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

 

[HallsofIvy]

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

No, you get -x^2+ x+ 30 but then your next is correct:

and the by -1 to get x^2-x-30=0 and then factor to get (x+5)(x-6).
Thank you everyone

Yes, that is correct.