A perfect-square trinomial is a three-term expression made by squaring a two-term expression. Find a number whose square gives the constant and whose double gives the coefficient of . Then graph the original and your candidate in Desmos to check that they overlap. Watch the sign of the middle term: squaring a difference produces a negative one.
Hints
- Hint 1
In , the last term is . What number could you square to get the constant in the given expression?
- Hint 2
Squaring produces two copies of , so its middle term is . Does twice the number you found give the coefficient of ?
Step-by-step
Spot the square and check its graph
Step 1Find the repeated number
A perfect-square trinomial follows . The same number must square to the last term and double to the middle coefficient. Here and , so fits both terms.
- Step 2
Graph the given expression
Type . Desmos draws the parabola, a U-shaped curve, for the given expression. Leave it on the graph to compare with the square you found.
- Step 3
Check the matching square
Type on the next line. Its curve overlaps the original. The square pattern also confirms an exact match: gives both and . So the expression equivalent to is . Choice D.