Find the equation of a quadratic function whose graph is a parabola passing thro

Chesley

Chesley

Answered question

2021-10-18

Find the equation of a quadratic function whose graph is a parabola passing through the points (0,2), (2,12), and (3,7).

Answer & Explanation

liingliing8

liingliing8

Skilled2021-10-19Added 95 answers

We have to find the equation of parabola passing through the points (0,2), (2,12), and (3,7).
Let the equation of parabola us y=f(x)=ax2+bx+c (1)
These equation satisfies the equation (0,2) passing through 2=0+0+c
c=2
substitute in (1)
y=ax2+bx2 (2)
(2,12) passing through (2)
12=a(2)2+b(2)2
12=4a2b2
4a2b=14
2ab=7 (3)
equation (2) passing through (3,7)
7=9a+3b2
9a+3b=9
3a+3=3 (4)
add (3) and (4)
2ab=73a+b=35a=10
a=2
substitute in (4)
3(2)+b=3
6+b=3
b=3
eqn (1) become
y=2x23x2
It is eqn of parabola

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