Chapter 2.4, Problem 21E

To determine

To find: To describe and correct the error in the writing an equation of the parabola.

Answer to Problem 21E

The error is in the second step, where one of the $x-$ intercept $-1$ is substituted as $1$ .

The equation of the parabola with the $x-$ intercepts $\text{-1and}2$ and passes through $(3,4)$ in intercept form is $y=(x+1)(x-2)$ .

Explanation of Solution

Given information: $x-$ intercepts $\text{-1and}2$ and passes through $(3,4)$ .

Intercept form of a parabola is $y=a(x-p)(x-q)$ .

  $x-$ Intercepts $p\text{and}q$ is $\text{-1and}2$ respectively.

By substituting the $x-$ intercepts in the intercept form of equation we get,

  $y=a(x+1)(x-2)$

To find the value of $a$ , substitute the point $(3,4)$ in the above equation.

  $\begin{array}{c}4=a(3+1)(3-2)\\ 4=a(4)(1)\\ 4=a(4)\\ a=1\end{array}$

Substitute $a=1$ in $y=a(x+1)(x-2)$ ,

  $y=(x+1)(x-2)$

The above equation is the correct intercept form of the given parabola.