D2 Explain the relationship between the x and y intercepts a

D2: Explain the relationship between the x and y intercepts and the general form of a quadratic function. Then demonstrate this relationship in the following:
a. Start with the intercepts and show how you can use these to find the general form.
b. Start with the general form and show how you can find the intercepts.

Solution

f(x) = ax^2 +bx + c ---- generaL form

x intercept : f(x) = 0 ; ax^2 +bx + c=0

yintercept : f(0) = c : Let this be y = c

x = (-b +/- sqrt(b^2 - 4ac))/2a

= ( -b +/- sqrt(b^2 - 4ay) )/2a

x = ( -b +/- sqrt(b^2 - 4ay) )/2a

x and y are the x intercept and y intercept

a) ax^2 + bx +c = f(x)

x intercepts are the roots of f(x) =0 ;

sum of roots : x1+x2 = -b/a ; x1*x2 = c/a

with y intercept f(0) = c

So, we have three unknowns a, b, c and 3 equations and we can find the

a,b,c and then f(x)

b) f(x) = ax^2 +bx +c

x intercept : plug f(x) = 0 and solve ax^2 +bx +c=0

y intercept : plug x=0 ; f(0) = c

So,