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slamgirl [31]
3 years ago
15

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
Mathematics
2 answers:
Ulleksa [173]3 years ago
8 0

Answer:

the answer is (a)

Step-by-step explanation: just did it

agasfer [191]3 years ago
4 0

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.}

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