Placing the turning point at wrong coordinates
"The Misplaced Vertex"
The Mistake in Action
For $y = x^2 - 4x + 3$, student states the minimum point is at $(0, 3)$.
Why It Happens
Students assume the turning point is at the y-intercept, or forget how to find the x-coordinate of the vertex.
The Fix
The turning point of $y = ax^2 + bx + c$ has x-coordinate: $$x = -\frac{b}{2a}$$
For $y = x^2 - 4x + 3$: $a = 1, b = -4$ $$x = -\frac{-4}{2(1)} = \frac{4}{2} = 2$$
Substitute to find y: $$y = (2)^2 - 4(2) + 3 = 4 - 8 + 3 = -1$$
Turning point: $(2, -1)$
Note: $(0, 3)$ is the y-intercept, not the vertex!
Spot the Mistake
Can you identify where this student went wrong?
$y = x^2 - 4x + 3$
minimum at $(0, 3)$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: