Chapter 2, Problem 15CR

To determine

To write: The equation of parabola with given points.

Answer to Problem 15CR

The equation of the parabola with the points $(-2,7),(1,10),\text{and}\left(2,27\right)$ is $y=4x^2+5x+1$ .

Explanation of Solution

Given information: A parabola passing through the points $(-2,7),(1,10),\text{and}\left(2,27\right)$ .

General form of the equation of a parabola is $y=a{x}^2+bx+c$ .

Equations of the parabola with the given points are

For the point $(-2,7)$ is $7=a{(-2)}^2+b(-2)+c\to 4a-2b+c=7$$\mathrm{...}(1)$

For the point $(1,10)$ is $10=a{(1)}^2+b(1)+c\to a+b+c=10$ $\mathrm{...}(2)$

For the point $(2,27)$ is $27=a{(2)}^2+b(2)+c\to 4a+2b+c=27$$\mathrm{...}(3)$

By solving the above three equations we get,

  $a=4,b=5,c=1$

Substitute $a=4,b=5,c=1$ in $y=a{x}^2+bx+c$ ,

  $y=4x^2+5x+1$

Therefore, the above equation is the equation of the parabola with the given points.