Chapter 1.1, Problem 19E

Solution

Describe and correct the error in analysis the graph of $y=4x^2+24x-7$ .

The x-coordinate of the vertex is: $x=-3$

Given:

The x-coordinate of the vertex is: $x=\frac{b}{2a}=\frac{24}{2(4)}=3$

Calculation:

The given function is $y=4x^2+24x-7$

Here $a=4,b=24,c=-7$

The graph of the given function $y=4x^2+24x-7$ is −

  

According to graph x-coordinate should be -3.

According to question-

The x-coordinate of the vertex is: $x=\frac{b}{2a}=\frac{24}{2(4)}=3$

Here error is that, x-coordinate of the vertex should be $x=\frac{-b}{2a}$ instead of $x=\frac{b}{2a}$ .

So, the correct x-coordinate of the vertex is: $x=\frac{-b}{2a}$

  $\begin{array}{l}x=\frac{-b}{2a}\\ =\frac{-24}{2(4)}\\ =\frac{-24}{8}\\ =-3\end{array}$