Question

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 6x plus 10 g(x) x g(x) 1 3

Answer 1

If we substitute 13 to f(x) and get a value for x, then the two equations will intersect. So,
f(x) = x^2 + 6x +10
13 = x^2 + 6x+ 10
x^2 + 6x - 3 = 0

Solving the quadratic equations:
The roots of the equation is
x = 0.4641 and
x = -6.4541

Therefore, the line will intersect with the quadratic function.

Answer 2

the complete question is

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 6x plus 10 g(x) x g(x) 1 3 2 5 3 7

we have

a quadratic function f(x)

`f(x)=x^(2) +6x+10`

a linear function g(x)

Let

`A(1,3)\\B(2,5)`

Find the slope AB

`m=((y2-y1))/((x2-x1))`

`m=((5-3))/((2-1))`

`m=2`

with
`m=2` and point A find the equation of the line

`y-y1=m*(x-x1)\\ y-3=2*(x-1)\\ y=2x-2+3\\ y=2x+1\\ g(x)=2x+1`

using a graph tool--------> graph f(x) and g(x)

see the attached figure

The graphs will not intersect

therefore

the answer is

No, they will not intersect