A quadratic already in vertex form, , shows its turning point without expanding. The square becomes at , so the vertex’s vertical coordinate is . Watch the coordinate the question asks for: the input that makes the square zero is the horizontal coordinate, not the vertical one.
Hints
- Hint 1
In vertex form, the square term becomes at the vertex. What value of makes the inside of the square, , equal ?
- Hint 2
A square cannot be negative, so making it gives this graph its lowest point. What output remains after the square term becomes ?
Step-by-step
Read the vertex from the square
Step 1Find where the square becomes zero
No Desmos needed. The function is already in vertex form. The vertex is where the parabola turns. Here, the square term is smallest when its inside is zero. Set the inside to zero:
Subtract :
- Step 2
Read the vertex’s vertical coordinate
At the vertex, the square term is . That leaves . Since a square cannot be negative, this is the lowest output. The vertex’s -coordinate is , not its input . Grid in -4.