identify the x coordinate in fx=-7x^2+3x+8

Question

I am asked to identify the x-coordinate in the fx format. Given fx=-7x^2+3x+8

I am given four possible solutions:

  -7/3    8    3/14     -3/7   

Answer 1

What I think this means is that if f(x) = –7x² + 3x + 8, check to see if f(x) = 0, where x is one of the four numbers that you listed above.

 

Here, f(x) represents a quadratic function. The fact that the sign of the leading term is negative indicates that the parabola (which is the graph of a quadratic function) opens downward. The solution(s) is the point or points on the x-axis where the graph intersects.

 

The most straight forward way to check if each number is a solution, is to plug the number into the function and see if the result is 0; if that result is 0, it would represent the x-coordinate of a solution of the equation:

 

For –7/3: f(–7/3) = (–7)(–7/3)² + 3(–7/3) + 8 = (–7)(49/9) – 7 + 8 = (–343/9) + 1 = –334/9 < 0. ×

 

For 8: f(8) = (–7)(8)² + 3(8) + 8 = (–7)(64) + 24 + 8 = –448 + 32 = –416 < 0. ×

 

For 3/14: f(3/14) = (–7)(3/14)² + 3(3/14) + 8 = (–7)(9/196) + 9/14 + 8 = –9/28 + 9/14 + 8 = 9/28 + 8 = 233/28 > 0. ×

 

For –3/7: f(–3/7) = (–7)(–3/7)² + 3(–3/7) + 8 = (–7)(9/49) – 9/7 + 8 = –63/49 – 9/7 + 8 = –63/49 – 63/49 + 392/49 = 266/49 > 0. ×

 

Not one of the four numbers gives a result of 0, so none of them is a solution of the equation.

 

Note: The graph of this function does have two distinct x-intercepts.

Answer 2

if you mean the x-intercept, then we are talking about the value of x that makes y=0 or we can also say f(x) = 0.  We say this because the x-intercept is the point where the graph of the function crosses the x axis and we know that the y=coordinate is zero for every point that lies on the x axis.

 

this function does not have an x-intercept so something is not correct with the question.