LEARN · EXPLAIN · REVISE

Calculate the discriminant.

Read the idea, work independently, then explain what changed.

TOPIC 01

Quadratic equations and functions

A negative discriminant does not mean there are no complex roots.

PREDICT → MOVE → EXPLAIN

Before moving a slider, predict the opening, vertex and intercepts. Then compare the graph with your prediction.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

x^2+2x+5=0

Working and explanation

BUILD THE REASONING

Hint 1

Use b²−4ac.

Hint 2

Here a=1,b=2,c=5.

Worked solution

Discriminant −16; no real roots.

Checks and common pitfalls: A negative discriminant does not mean there are no complex roots.

Think first. Reveal a hint when the class is ready.