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

the answer is (a)

Step-by-step explanation: just did it

Answer 2

Consider the quadratic function
`f(x)=(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 (1)/(3)x^2-2x=x\\ \\ \Rightarrow (1)/(3)x^2-3x=0\\ \\ \Rightarrow x\left ( (1)/(3)x-3 \right )=0\\ \\ \text{now using the zero product rule, we get}\\ \\ x=0 , \text{ and } (1)/(3)x-3=0`

`\Rightarrow x=0, \text{ and }(1)/(3)x=3\\ \\ \Rightarrow x=0, \text{ and }x=9\\ \\ \text{so the functions intersect at x=0 and x=9.}`