Chapter 4.7, Problem 49HP

To determine

To find: the parabola when the three points are mentioned on graph.

Answer to Problem 49HP

The parabola is $a{x}^2+bx+c=0$ .

Explanation of Solution

Given information:

The three points are $\left(a_{0,}{b}_0\right),\left(a_1,b_1\right),\left(a_2,b_2\right)$ where $\left(a_0,b_0\right)$ is any integer.

Formula:

To solve the all three unknown equations.

Calculation:

Consider the quadratic equation $a{x}^2+bx+c=0$ also the points are $\left(a_{0,}{b}_0\right),\left(a_1,b_1\right),\left(a_2,b_2\right)$ .

Now we will substitute the points in the above quadratic equation.

Therefore the equation will become as mentioned below.

  $\begin{array}{l}a{a}_0{}^2+b{b}_0+c=\mathrm{0........}\left(i\right).\\ a{a}_1{}^2+b{b}_1+c=\mathrm{0........}\left(ii\right).\\ a{a}_2{}^2+b{b}_2+c=\mathrm{0........}\left(iii\right).\end{array}$

Recall that we have to solve the all three unknown equations to find the value of $a,b,c$ .

Then we will substitute the value in the quadratic equation $a{x}^2+bx+c=0$ to get the equation of parabola.