A quadratic in vertex form, , shows its turning point without expanding. The squared part is zero at the vertex, so find the input that makes it zero, then read the output. Graph the function in Desmos and click the vertex to check. Watch the sign inside the parentheses: it is opposite the vertex’s -coordinate.
Hints
- Hint 1
In vertex form, the vertex is the turning point of the graph. A square cannot be negative, so this upward-opening graph reaches its lowest point when the squared part equals . What input makes that happen?
- Hint 2
The sign inside can be misleading. Set what’s inside the square equal to to find the input. Then graph the function in Desmos and click its lowest point to read both coordinates.
Step-by-step
Find where the square is zero
Step 1Use the form of the function
The function is in vertex form: a squared expression followed by a constant. Its squared part has a positive coefficient, so the graph opens upward. A square cannot be negative, so the vertex is where the squared part is zero.
- Step 2
Find the vertex’s input
Set what’s inside the square equal to :
Add to both sides:
The minus sign inside the parentheses does not make the vertex’s -coordinate negative.
- Step 3
Read the vertex on the graph
Type in Desmos and click the lowest point. Desmos shows . The is the output when the square is , so the vertex is . Choice A.