Find the value of c such that the point (4,2) lies in the graph of f(x)= cx^2+3x-4.
To find the value of c such that the point (4, 2) lies on the graph of f(x) = cx^2 + 3x - 4, we need to substitute the coordinates of the point into the equation and check if the equation holds true.
Substituting x = 4 and y = 2 into the equation f(x), we get:
f(4) = c(4)^2 + 3(4) - 4
f(4) = 16c + 12 - 4
f(4) = 16c + 8
Since we want the point (4, 2) to lie on the graph of f(x), the y-coordinate of the point should be equal to f(4). Therefore, we have:
f(4) = 2
Substituting this into the equation above, we obtain:
2 = 16c + 8
Next, we isolate the term with c:
16c = 2 - 8
16c = -6
Finally, we solve for c:
c = -6/16
c = -3/8
Therefore, the value of c such that the point (4, 2) lies in the graph of f(x) = cx^2 + 3x - 4 is -3/8.
F(x) = CX^2 + 3X - 4.
Xv = -b/2a = -3 / 2c = 4,
-3 / 2c = 4,
c = -3/8.