SOLUTION: I need to write a quadratic function in standard form for a parabola shown. It gives me three different point on the parabola which are (2,7), (3,2), and (5,4). What is the andswer

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I need to write a quadratic function in standard form for a parabola shown. It gives me three different point on the parabola which are (2,7), (3,2), and (5,4). What is the andswer      Log On


   

Question 366152: I need to write a quadratic function in standard form for a parabola shown. It gives me three different point on the parabola which are (2,7), (3,2), and (5,4). What is the andswer and how am I supposed to get the answer? And the parabola opens up.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the general form of a quadratic equation.
y=ax%5E2%2Bbx%2Bc
7=a%282%29%5E2%2Bb%282%29%2Bc
1.highlight%284a%2B2b%2Bc=7%29
.
.
2=a%283%29%5E2%2Bb%283%29%2Bc
2.highlight%289a%2B3b%2Bc=2%29
.
.
4=a%285%29%5E2%2Bb%285%29%2Bc
3.highlight%2825a%2B5b%2Bc=4%29
.
.
.
Now you have three linear equations in three unknowns (a,b,c).
Solve using any method (substitution, elimination, matrix methods).
.
.
.

.
.
.
It looks like the parabola opens upwards.