Chapter 8, Problem 26CR

To determine

To graph: The cubic function using zeros.

Explanation of Solution

Given information: The quadratic function $f(x)=x^2+x-2$

Graph:

Let’s find vertex and x intercepts. Where ‘ a’ is coefficient of $x^2$ term and ‘ b’ is coefficient of x term.

  $a=1$ ; $b=1$

Plug in these values into formula $\frac{-b}{2a}=\frac{-1}{2(1)}=-0.5$

Now let’s find corresponding y value.

  $y={(-0.5)}^2+(-0.5)-2$

  $y=0.25-0.5-2$

  $y=-2.25$

So, vertex is (-0.5, -2.25)

Now, let’s find the x intercepts.

At x intercepts the value of y is 0

  $x^2+x-2=0$

Factor it by finding two integers whose multiplication is -2 but adds to 1.

Here, 2 and -1 works because $2\times -1=-2$ and $2-1=1$

Factored form is $(x+2)(x-1)=0$

Using zero product property

  $x+2=0$ , $x-1=0$

Solve each equation for ‘ x’

  $\begin{array}{l}x=-2\\ x=1\end{array}$

Now, vertex is at (-0.5, -2.25) and x intercepts are (-2,0) and (1,0). Represent these points on xy plane to graph it.

  

Interpretation: The graph is open up parabola and the vertex is the minimum.