How to find the formula of a quadratic function knowing

pozicijombx

pozicijombx

Answered question

2022-01-20

How to find the formula of a quadratic function knowing that it contains the points (2, 2) and (0, 1) and (1, 2.5)?

Answer & Explanation

Brenton Pennington

Brenton Pennington

Beginner2022-01-21Added 15 answers

Step 1
y=ax2+bx+c
Find a, b, and c.
Write that this graph passes at the 3 points: (2, 2); (0, 1) and (1, 2.5).
2=4a2b+c
1=c
2.5=a+b+c
Solve this system of linear equations.
First c=11=4a2b4a2b=1
3.5=a+b2a+2b=7
Step 2
6a=6a=1
a+b=3.5b=3.5+1=2.5
Finally the quadratic function is:
y=x22.5×x+1
Check:
x=2y=4+5+1=2 Correct
x=1y=12.5+1=2.5 Correct

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