Question

Use the graph that shows the solution to f(x)=g(x) . f(x)=−3/4x2+3x+1 g(x)=2x What is the solution to f(x)=g(x) ?

Answer 1

Answer:

k12

3.03: Intersections of Graphs quiz

The answer is x=0 and x=2

Step-by-step explanation:

Answer 2

Option C: $x=2$ is the solution of the graph.

Explanation:

The function is $f(x)=-\frac{3}{4}x^{2} +3x+1$ and $g(x)=2x$

We need to determine the solution of the function.

The solution can be determined by equating $f(x)=g(x)$

Thus, we have,

$-\frac{3}{4}x^{2} +3x+1=2x$

Subtracting both sides by 2x, we have,

$-\frac{3}{4}x^{2} +x+1=0$

Multiplying both sides by 4, we have,

$-3x^{2} +4x+4=0$

Factoring, we get,

$-3x^{2} +6x-2x+4=0$

Factoring out the common terms, we have,

$(-3x^{2} +6x)+(-2x+4)=0$

Simplifying, we get,

$-3x(x-2)-2(x-2)=0$

       $(-3x-2)(x-2)=0$

Thus, we have,

$-3x-2=0$  or $x-2=0$

Simplifying, we get,

$x=-\frac{2}{3}$  or  $x=2$

Thus, the solution of the graph is $x=2$

Therefore, Option C is the correct answer.