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

Yes they will intersect.

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=(y_2-y_1)/(x_2-x_1)`

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

`m=(1-0)/(-3-(-1))`

`m=(1)/(-2)`

`m=-(1)/(2)`

The equation form is
`g(x) =-(1)/(2)x +c`

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

`2=-(1)/(2)(-5) +c`

`2=(5)/(2)+c`

`2-(5)/(2)=c`

`c=(-1)/(2)`

The the equation of g(x) is
`g(x) =-(1)/(2)x-(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)=-(1)/(2)x-(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.