maths question - leaving cert algebra

ublinina

Can anybody help with this leaving cert maths question. its algebra part c .

The quadratic equation f(x) = ax^2+ bx +c is shown , where a>0 ( a diagram of a quadratic curve is shown with the curve touching the x axis at point p ).

The curve touches the x-axis at the point p.

Find the co-ordinates of the point p in terms of a and b

Young Siward

Hi,

First of all i'm probably competely wrong here....

First of all if the graph touches at one point only, then there's only one root.
So b^2-4ac=0.
therefore....b^2=4ac

With this in mind, you can sub this into the quadratic formula to get x, this cancels out the square root part so you get (-b)/2a for x.

So your answer should be (-b/2a,0)!

I'm well rusty at this stuff, someone else?

DS

Yeah that's right.
f(x) = 0 at x = p
f(p) = 0
ap^2 + bp + c = 0
Use -b formula. You know there's only one value of x so b^2 - 4ac must = 0. That leaves you with -b/2a. Obviously the y coordinate is 0.

bp_me

What year was the question? All the solutions are available online - http://www.education.ie.

ublinina

Thanks for the help
That seems to be the correct answer.
(-b/2a)..