The standard form of a quadratic function is given below. Select ALL statements which MUST be true about its graph.

f (x) = ax? + bx + c

A. The y-intercept of the graph is at (0,c).

B. The graph has an x-intercept at (c,0).

C. When "a" is positive, the graph opens up.

D. The graph always has two distinct x-intercepts,

A; C.

Step-by-step explanation:

B. not correct: the graph can have no interception; one interception or two interception;

D. not correct: the graph can have no interception; one interception or two interception.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.