pozicijombx

## Answered question

2022-01-20

How to find the formula of a quadratic function knowing that it contains the points and and ?

### Answer & Explanation

Brenton Pennington

Beginner2022-01-21Added 15 answers

Step 1
$y=a{x}^{2}+bx+c$
Find a, b, and c.
Write that this graph passes at the 3 points: and .
$2=4a-2b+c$
$1=c$
$-2.5=a+b+c$
Solve this system of linear equations.
First $c=1\to 1=4a-2b\to 4a-2b=1$
$-3.5=a+b\to 2a+2b=-7$
Step 2
$6a=-6\to a=-1$
$a+b=-3.5\to b=-3.5+1=-2.5$
Finally the quadratic function is:
$y=-{x}^{2}-2.5×x+1$
Check:
$x=-2\to y=-4+5+1=2$ Correct
$x=1\to y=-1-2.5+1=2.5$ Correct

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