0- Find the x-intercepts of y = 4x2 – 2x – 5.
First off, remember that finding the x-intercepts means setting y equal to zero and solving for the x-values, so this question is really asking you to "Solve 4x2 – 2x – 5 = 0".
| This is the original problem. | 4x2 – 2x – 5 = 0 |
| Move the loose number over to the other side. | 4x2 – 2x = 5 |
| Divide through by whatever is multiplied on the squared term. Take half of the coefficient (don't forget the sign!) of the x-term, and square it. Add this square to both sides of the equation. Convert the left-hand side to squared form, and simplify the right-hand side. (This is where you use that sign that you kept track of earlier. You plug it into the middle of the parenthetical part.) | x2-(1/2)x=(5/4) (-1/4)2=(1/16) x2-(1/2)x+(1/16)=(5/4)+(1/16) (x-(1/4))2=(21/16)
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| Square-root both sides, remembering the"±" on the right-hand side. Simplify as necessary. | x=(1/4)+0r-sqrt(21)/4 |
| Solve for "x =". | x=(1/4)+0r-sqrt(21)/4 |
| Remember that the "±" means that you have two values for x. |
The answer can also be written in rounded form as -0.89 and 1.39
