Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places.

A) 0.574
B) 0.564
C) 0.569
D) 0.519
E) 0.619

Question

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places. ​   ​
​  ​
A) ​0.574 
B) ​0.564 
C) ​0.569 
D) ​0.519 
E) ​0.619

Quizplus · Accepted Answer

To find the x-value of the point of intersection, we need to solve for x in the equation f(x) = g(x).

First, let's simplify the equations:

f(x) = 2x^2 - x - 3 
g(x) = 3x - 1

Setting them equal to each other: 
2x^2 - x - 3 = 3x - 1

Bringing all the terms to one side: 
2x^2 - 4x - 2 = 0

Dividing both sides by 2: 
x^2 - 2x - 1 = 0

Using the quadratic formula:

x = [2 ± sqrt(4 + 4)]/2 
x = 1 ± sqrt(2)

Rounding to three decimal places:

x ≈ 0.569

Therefore, the best choice is C.

Approximate,to Three Decimal Places,the X-Value of the Point of Intersection