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Chapter 9: Q. 520 (page 987)

In the following exercises, solve graphically and write the solution in interval notation:

x2+4x+3≤0

Short Answer

Expert verified

The solution to the given inequality is -3,-1.

Step by step solution

01

Step 1. Given information.

We have:

x2+4x+3≤0

02

Step 2. Find the vertex of the function. 

The vertex of an up-down facing parabola of the form y=ax2+bx+c is xv=-b2a

The parabola params are:a=1, b=4, c=3xv=-b2axv=-42· 1xv=-2

Substitute xv=-2in the given equation to find yv:

yv=-1Therefore the parabola vertex is-2, -1

03

Step 3. Find the x-intercept. 

Substitute y=f(x)=0:


x2+4x+3=0For a quadratic equation of the form ax2+bx+c=0 the solutions are x1, 2=-b±b2-4ac2aFor a=1, b=4, c=3x1, 2=-4±42-4· 1· 32· 1x1, 2=-4± 22· 1x=-1, x=-3

X Intercepts: -1, 0, -3, 0

04

Step 4. Find the solution by drawing the figure. 

Plot the vertex of the function at -2, -1with intercepts then draw the curve passes through the plotted points:

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