Find the quadratic function y = ax^{2} + bx +

lilyta79jd

lilyta79jd

Answered question

2021-12-03

Find the quadratic function y=ax2+bx+c whose graph passes through the given points: (1, 3), (3, 25), (2, 5)
[Hint: Substitute each point into y=ax2+bx+c to get a system of linear equations, then solve.]

Answer & Explanation

Ourst1977

Ourst1977

Beginner2021-12-04Added 21 answers

Step 1
Given:
(1, 3), (3, 25), (2, 5)
y=ax2+bx+c
Step 2
Substitute y=3 and x=1 as,
3=a(1)2+b(1)+c
1) 3=ab+c
Substitute y=25 and dx=3 as,
25=a(3)2+b(3)+c
2) 25=9a+3b+c
Substitute y=5 and x=2 as,
5=a(2)2+b(2)+c
3) 5=4a2b+c
Step 3
Solve the system of equation,
1) 3=ab+c
2) 25=9a+3b+c
3) 5=4a2b+c
Solve (1) for c as,
3=ab+c
c=a+b3
Substitute (a+b3) for c in (2) as,
25=9a+3b+(a+b3)
25=8a+4b±3
4) 8a+4b=28
Substitute (a+b3) for c in (3) as,
5=4a2b+(a+b3)
5=3ab3
8=3ab
5) 3ab=8
Solve the equation (5) for b as,
3ab=8
b=3a8
Substitute 3a8 for b in (4) as,
8a4(3a8)=28
8a+12a32=28
20a=60
a=3
Substitute 3 for a in (5) as,
3(3)b=8
9b=8
b=98
b=1
Substitute 3 for a and 1 for b in (1) as,
3=ab+c
3=31+c
c=32
c=5
Hence, the value of

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