Question

For the function f(x)=8x^2−18x+5, use f(x)=−4 to find two points that lie on the graph of the function.

Answer 1

Answer:

  (3/4, -4), (3/2, -4)

Step-by-step explanation:

We want to find values of x such that f(x) = -4:

  -4 = 8x^2 -18x +5 . . . . . . . . set f(x) = -4

  -9 = 8(x^2 -9/4x) . . . . . . . subtract 5, factor out the leading coefficient

  -9 +8(9/8)^2 = 8(x^2 -9/4x +(9/8)^2) . . . . complete the square

  9/8 = 8(x -9/8)^2 . . . . simplify, write as a square

  ±√(9/8) = x -9/8 . . . . . . divide by 8, take the square root

  x = 9/8 ± 3/8 = {6/8, 12/8} = {3/4, 3/2} . . . . . add 9/8 and simplify

These are the x-coordinates of the points with y-coordinate -4.

Two points are (3/4, -4) and (3/2, -4).