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jolli1 [7]
3 years ago
6

(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

Mathematics
2 answers:
Margaret [11]3 years ago
8 0

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.

schepotkina [342]3 years ago
5 0
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. 
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