Home > INT3 > Chapter 11 > Lesson 11.2.4 > Problem11-108

11-108.

Write the equation in standard form of the parabola that passes through the points $\left(1, 5\right), \left(3, 19\right)$, and $\left(–2, 29\right)$.

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

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

You have created a system of three equations with three variables. Solve the system of equations.
Refer to problem 11-100 for help.

$a + b + c = 5$
$9a + 3b + c = 19$
$4 − 2b + c = 29$

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

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