Chapter 8.8, Problem 2CE

To determine

Calculate the vortex of the given algebraic function and draw a sketch.

Answer to Problem 2CE

The solution is

  $vortex=\left(1,3\right)$

  

Explanation of Solution

Given: The function is given

  $f(x)=-x^2+2x+2$

Calculation:

The algebraic function in the quadratic form

  $a{x}^2+bx+c$

In the comparison

  $a=1;b=2;c=2$

Calculate the vortex

  $vortex=\left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)$

After simplifying we will get the solution

  $vortex=\left(1,3\right)$

program:

clc
clear
close all
% syms x
f=@(x) -x^2+2*x+2; %%% a quadratic equation a*x^2+b*x+c
a=-1;b=2;c=2;
vortex=[-b./2*a  f(-b./2*a)]
p=ezplot(f);
p.LineWidth=1.2;
set(gca,'linewidth',1.2,'Fontsize',12)
ylabel('f(x)')
axis square

Query:

• First, we have defined the given algebraic relation.
• Compare with the quadratic equation.
• Then find the value of a, b, and c.
• The calculate the vortex.
• Sketch a figure.