Question

Find a quadratic function that includes the set of values below: (0,5), (2,15), (4,9) The equation of the parabola is y = ___.

Transformations of functions
ANSWERED
asked 2021-05-16
Find a quadratic function that includes the set of values below: (0,5), (2,15), (4,9)
The equation of the parabola is y = ___.

Answers (1)

2021-05-17
Let y=ax^2+bx+c be the equation of the parabola. Set up equations.
Using (0,5). \(\displaystyle{5}={a}{\left({0}\right)}^{{2}}+{b}{\left({0}\right)}+{c}\)
Using (2,15), \(\displaystyle{15}={a}{\left({2}\right)}^{{2}}+{b}{\left({2}\right)}+{5}\)
4a+2b=10
2a+b=5
Using (4,9)
\(\displaystyle{9}={a}{\left({4}\right)}^{{2}}+{b}{\left({4}\right)}+{5}\)
16a+4b=4
4a+b=1
Subtract each side of (1) and (2) to eliminate b and solve for a: -2a=4
a=-2
Solve for b using (1): 2(-2)+b=5
-4+b=5
b=9
So, the equation is \(\displaystyle{y}=-{2}{x}^{{2}}+{9}{x}+{5}\)
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