A quadratic in vertex form has a squared expression that shows where its graph turns. Find the input that makes the square , then read the output at that point. You can check by graphing the function in Desmos and clicking its turning point. Watch the sign inside the parentheses: it is not automatically the vertex’s -coordinate.
Hints
- Hint 1
The vertex is where the parabola turns. A square reaches its smallest value at , so start with the expression inside the square. What input makes it ?
- Hint 2
Once you have that input, graph the quadratic in Desmos and click its turning point. Read both coordinates: the first is the input, and the second is the function’s output.
Step-by-step
Find where the square is zero
Step 1Find the vertex’s input
The vertex is the turning point of a parabola, the U-shaped graph of a quadratic. Here is positive, so the squared part is smallest when it equals . Make the inside of the square equal , then add :
The minus sign inside gives , not .
- Step 2
Read the turning point
Type in Desmos. Click the curve, then its lowest marked point. Desmos labels it , so the vertex of is . The positive makes this point the minimum, or lowest point. Choice D.