Finding the function`s expression

Question

I have a quadratic equation and I know that the x-intercepts are -2 and 5. How do I determine the function`s expression (find out what a, b and c are)?

I`m norwegian so I don`t know all the english terms, but I hope you understand

Answer 1

Use the factored form of a quadratic expression:

 

a(x-p)(x-q)

• a = a constant
• p and p are the x-intercepts = -2 and 5

 

a(x+2)(x-5)

 

There are an infinite number of parabolas that have these two intercepts, so a could be any number.  To figure out what value a actually has, you would need one additional point on the graph.  Without that point, a could be any number (so assume it's a=1).

 Multiply the above expression out to put it into standard (ax²+bx+c) form.