Chapter 3, Problem 11CR

To determine

To calculate : The equation in standard form $y=a{x}^2+b$ whose graph passes through the points $\left(-1,1\right)$ and $\left(2,7\right)$

Answer to Problem 11CR

Equation is $y=2x^2-1$

Option “D” is correct.

Explanation of Solution

Given information : The given points are:

  $\left(-1,1\right)$ And $\left(2,7\right)$

Formula used : Substituting the points.

Calculation : Now, we substitute the given points in equation $y=a{x}^2+b$ we get,

Putting $\left(-1,1\right)$ in equation $y=a{x}^2+b$

  $1=a+b$

Putting $\left(2,7\right)$ in equation $y=a{x}^2+b$

  $7=4a+b$

On solving above two equations we get

  $6=3a$ (Subtracting the $1=a+b$ from $7=4a+b$ )

  $a=2$

Since, $1=a+b$

  $1=2+b$

  $b=-1$

Putting values of $a$ and $b$ in, equation $y=a{x}^2+b$

Equation is $y=2x^2-1$