What is the equation of a quadratic function whose graph passes through \left

facas9 2021-10-24 Answered
What is the equation of a quadratic function whose graph passes through (2,0), (5,0), and (3,8)? Write your equation in standard form.
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Expert Answer

okomgcae
Answered 2021-10-25 Author has 93 answers
Consider the given:
The graph passes through (2,0), (5,0) and (3,8).
Let the equation is y=ax2+bx+c.
Consider the point (2,0),
a(2)2+b(2)+c=0
4a+2b+c=0 ... ... (1)
Consider the point (5,0),
a(5)2+b(5)+c=0
25a+5b+c=0 ... ... (2)
Consider the point (3,8),
a(3)2+b(3)+c=8
9a+3b+c=8 ... ... (3)
From equation (1) and (2),
4a+2b+c=25a+5b+c
4a+2b=25a+5b
a25a=5b2b
7a=b
From equation (1),
4a+2b+c=0
4a+2(7a)+c=0
4a14a+c=0
10a+c=0
c=10a
Substitute the value of b and c in equation (3).
9a+3b+c=8
9a+3(7a)+(10a)=8
9a21a+10a=8
21a+19a=8
2a=8
a=4
b=7a
b=7(4)
b=28
c=10a
c=10(4)
c=40
Hence, The equation of quadratic function will be:
y=4x228x+40
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