LEARN · EXPLAIN · REVISE

How many distinct real roots does this equation have?

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

TOPIC 01

Quadratic equations and functions

The whole graph lies above the x-axis. A negative discriminant does not mean the function is negative.

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 / Standard#Your turn

x^2+4x+8=0

Working and explanation

BUILD THE REASONING

Hint 1

Compute b² − 4ac, using the sign of each coefficient.

Hint 2

Alternatively, complete the square and compare its minimum with zero.

Worked solution

D: there are no real roots.

Checks and common pitfalls: The whole graph lies above the x-axis. A negative discriminant does not mean the function is negative.

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