Today is rung 8 of 10 on this topic
Quadratic equations and their graphs
Can do: Solves quadratics by factoring, completing the square and the formula, and connects roots to the graph.
Why it matters
The link between the algebraic solution and the x-intercepts is the conceptual heart of it — without it, quadratics are three unrelated procedures.
What it looks like when it's wobbly
Applies the formula without noticing it factors easily, and doesn't see the roots on the graph.
⏱️ Two-minute check
"Solve x² − 5x + 6 = 0 and sketch it. Where do your solutions appear on the sketch?"
Solid looks like: x = 2 and 3, and both marked as x-intercepts.
The full activity for this topic · 30 minutes
Roots Are Where It Crosses
- 1Solve a quadratic algebraically and note the roots.
- 2Graph it and mark where it crosses the x-axis. Same numbers.
- 3Try one with no real roots and see the parabola miss the axis entirely.
- 4Find the vertex and interpret it in a real context — maximum height, minimum cost.
- 5Model a real projectile with a quadratic and answer a question with it.
If it's too hard
Factorable quadratics with integer roots.
If it's too easy
Complete the square to find the vertex, and interpret the discriminant.
Say this
"Your two answers — where are they on the picture? That's what solving actually means."