Home > CCA2 > Chapter 6 > Lesson 6.1.5 > Problem6-72

6-72.

Find the equation in $y=ax^2+bx+c$ form of the parabola that passes through the points $(1,5),(3,19),\ \text{and}\ (−2,29)$.

Substitute the point $(1,5)$ into $y=ax^2+bx+c$ where $x=1$ and $y=5$.

Repeat the previous step with $(3,19)$ and $(−2,29)$ to create two more equations.

You have created a system of three equations with three variables. Solve the system of equations.
Refer to problem 6-71 for help.

$a+b+c=5\\9a+3b+c=19\\4−2b+c=29$

$(a,b,c)=(3,−5,7)$. Substitute for a, b, and c to find the equation of the parabola.

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