SOLUTION: The graph of a quadratic function passes through B(4,6), and the zeros of the function are 5 and 6. Write an equation of the graph in general form. This question makes no sen

Algebra ->  Graphs -> SOLUTION: The graph of a quadratic function passes through B(4,6), and the zeros of the function are 5 and 6. Write an equation of the graph in general form. This question makes no sen      Log On


   

Question 759456: The graph of a quadratic function passes through B(4,6), and the zeros of the function are 5 and 6. Write an equation of the graph in general form.
This question makes no sense. If the x-intercepts are 5 and 6 how can there be a point (4,6) and still be a quadratic function. HELP please.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Generally you would have y=ax^2+bx+c, and you are given the two zeros of the parabola. Try to narrow some of the equation using them.

Point (5,0):
0=a%2A5%2A5%2Bb%2A5%2Bc
25a%2B5b%2Bc=0

Point (6,0):
a%2A6%2A6%2Bb%2A6%2Bc=0
36a%2B6b%2Bc=0

Also you were given point B(4,6):
a%2A4%2A4%2Bb%2A4%2Bc=6
16a%2B4b%2Bc=6

NOW you have a system of three equations in three unknowns (yes, they should be constants but currently you do not know their values) of a, b, and c.
---------------------
SYSTEM:
16a%2B4b%2Bc=6
36a%2B6b%2Bc=0
25a%2B5b%2Bc=0
---------------------

Can you take the rest of the solution process from there?


Omitting the steps in solving that system, I found:
a=3
b=-33
c=90
EQUATION: highlight%28y=3x%5E2-33x%2B90%29
{solution checks as correct}.