Question

Betsy is analyzing a quadratic function f(x) and a linear function g(x). Will they intersect? f(x) g(x) graph of the function f of x equals one third times x squared, minus 2 x g(x) 1 1 2 2 3 3

Answer 1

Consider the quadratic function $f(x)=\frac{1}{3}x^2-2x$

and the linear function g(x) defined as

$\text{at  }x=1, g(x)=1; \text{ at }x=2, g(x)=2 \text{ and at }x=3, g(x)=3$

$\text{so the linear function is } g(x)=x\\ \\ \text{now to check whehter the quadratic function f(x) and linear function }g(x)\\ \text{intersects, we solve the equations }f(x)=g(x)\\ \\ \Rightarrow \frac{1}{3}x^2-2x=x\\ \\ \Rightarrow \frac{1}{3}x^2-3x=0\\ \\ \Rightarrow x\left ( \frac{1}{3}x-3 \right )=0\\ \\ \text{now using the zero product rule, we get}\\ \\ x=0 , \text{ and } \frac{1}{3}x-3=0$

$\Rightarrow x=0, \text{ and }\frac{1}{3}x=3\\ \\ \Rightarrow x=0, \text{ and }x=9\\ \\ \text{so the functions intersect at x=0 and x=9.}$

Answer 2

Answer:

the answer is (a)

Step-by-step explanation: just did it