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

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 $$\displaystyle{y}=-{2}{x}^{{2}}+{9}{x}+{5}$$