LEARN · EXPLAIN · REVISE

Find the maximum value over real x.

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

TOPIC 01

Quadratic equations and functions

The sign of the leading coefficient determines whether the vertex is a maximum or minimum.

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

y=-2(x-1)^2+8

Working and explanation

BUILD THE REASONING

Hint 1

A real square is nonnegative.

Hint 2

Multiplication by −2 makes the squared term nonpositive.

Worked solution

Maximum 8 at x=1.

Checks and common pitfalls: The sign of the leading coefficient determines whether the vertex is a maximum or minimum.

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