Question 958·Easy·Math

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3\,(x - 2)^2 + y = 5

The equation above relates the variables $x$ and $y$ . Which expression gives $y$ in terms of $x$ ?

A formula question asking for $y$ “in terms of $x$ ” is about isolating $y$ : get $y$ alone and leave $x$ in the result. Graph the given equation in Desmos to see how $y$ changes as $(x-2)^2$ grows. Then subtract the entire term added to $y$ from both sides. Watch for the minus sign when that term moves.

Hints

Hint 1
To express $y$ in terms of $x$ , get $y$ alone while leaving $x$ in the formula. Which term is added to $y$ in the given equation?
Hint 2
An equation stays balanced when you do the same thing to both sides. The added term is all of $3(x-2)^2$ ; subtract that whole term, not only the $3$ .

Step-by-step

Subtract the term added to y
Step 1
Check the graph’s direction
Type $3(x-2)^2+y=5$ in Desmos. Its graph falls on either side of $x=2$ . As $(x-2)^2$ grows, $y$ must shrink to keep the sum at $5$ , so expect a negative squared term when $y$ is alone.
Step 2
Subtract the whole squared term
To leave $y$ alone, subtract the entire $3(x-2)^2$ from both sides, not $x-2$ by itself:
$3(x-2)^2+y-3(x-2)^2=5-3(x-2)^2.$
Step 3
Cancel and identify the expression
Cancel the opposite copies of $3(x-2)^2$ on the left: $y=5-3(x-2)^2$ . The negative squared term matches the falling graph, and $y$ is now in terms of $x$ . Choice D.

Lessons that teach this

SAT Advanced AlgebraIntermediateCoreRearrange nonlinear formulas

Question 958·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this