Find the equation of the quadratic function that passes through the points \l

glasskerfu

glasskerfu

Answered question

2021-11-05

Find the equation of the quadratic function that passes through the points (3,0), (2,0), and (0,30). Write your answer in standard form.

Answer & Explanation

irwchh

irwchh

Skilled2021-11-06Added 102 answers

We have to find the equation of the quadratic function that passes through the points (3,0), (2,0), and (0,30).
let the equation of the quadratic function be:
y=ax2+bx+c
since the curve passes through the points (3,0), (2,0), and (0,30).
therefore it must satisfy the equation of the curve.
therefore,
0=a(3)2+b(3)+c
0=9a3b+c (1)
0=a(2)2+b(2)+c
0=4a+2b+c (2)
30=a(0)2+b(0)+c
30=c (3)
therefore we get c=30.
now substitute the value of c=30 in the equation (1) and (2).
therefore,
9a3b30=0 (4)
4a+2b30=0 (5)
now solve the equation (4) and (5) to find the value of a and b.
multiply the equation (4) by 2 and equation (5) by 3 and then add both equations.
therefore,
18a6b60+12a+6b90=0
30a150=0
30a=150
a=5
now substitute the value of the a in the equation (4) to get the value of b.
therefore,
9(5)3b30=0
453b30=0
15=3b
b=5
therefore the value of a is 5, value of b is 5 and value of c is -30.
now substitute the values a,b and c in the quadratic function.
therefore,
y=ax2+bx+c
=5x2+5x30
therefore the equation of the quadratic function in standard form that passes through the given points is
y=5x2+5x30

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