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

$m=\frac{(y2-y1)}{(x2-x1)}$

$m=\frac{(5-3)}{(2-1)}$

$m=2$

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