Question

(06.05) Neil is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect? graph of the function f of x equals x squared plus 4 x plus 4 g(x) x g(x) −1 0 −3 1 −5 2

Answer 1

Answer:

Yes they will intersect.

Step-by-step explanation:

Given : Neil is analyzing a quadratic function f(x) and a linear function g(x).

$f(x)=x^2+4x+4$ and

x       -1      -3     -5

g(x)    0      1       2

To find : Will they intersect?

Solution :

Given Points for g(x) are (-1,0) , (-3,1) and (-5,2).

As g is a linear function,

Then it must be in form of g(x) = mx +c

where, c is constant and m is slope.

Using slope formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Here, $x_1=-1 , x_2=-3 , y_1=0, y_2=1$

$m=\frac{1-0}{-3-(-1)}$

$m=\frac{1}{-2}$

$m=-\frac{1}{2}$

The equation form is $g(x) =-\frac{1}{2}x +c$

Now, Put (-5,2) point as it also satisfy the equation

$2=-\frac{1}{2}(-5) +c$

$2=\frac{5}{2}+c$

$2-\frac{5}{2}=c$

$c=\frac{-1}{2}$

The the equation of g(x) is $g(x) =-\frac{1}{2}x-\frac{1}{2}$

Now, We plot the equation of f(x) and g(x) in graphing tool.

The function $f(x)=x^2+4x+4$ is plotted by red curve.

The function $g(x)=-\frac{1}{2}x-\frac{1}{2}$ is plotted by blue curve.

The intersection point of both the curve is (-3,1) and (-1.5,0.25).

Therefore, Yes the function intersect.

Refer the attached figure below.

Answer 2

Given the stated equation we know that that quadratic formula has 2 as its degree. This meats it has 2 roots. A linear equation has a degree of 1. A linear equation has 1 root. To know if they intersect, the must have one root in common. To know this, solve the two equation simultaneously. If they result to an answer then they intersect.