Quadratic Graphs

Chapter summary, hard words and model exam answers for ICSE Class 10 Hindi.

Free online summary and notes (ICSE Class 10 Hindi). Read it here, no PDF download needed.

About the author

Mathematics · CBSE 10 · ICSE 10 · GCSE (AQA, Edexcel, OCR)

If a is positive it opens up like a smile (lowest point at the vertex). If a is negative it opens down like a frown (highest point).

Substitute that x back into the equation for the y-value. The vertex sits exactly on the axis of symmetry, the mirror line down the middle.

Factorise, complete the square, or use the formula. A parabola may cross twice, just touch once, or miss the x-axis entirely.

Positive means two crossings, zero means it just touches, negative means it never reaches the x-axis.

parabola	the symmetric U-shaped (or inverted U) curve drawn by a quadratic
vertex	the turning point of a parabola: minimum if it opens up, maximum if it opens down
axis of symmetry	the vertical mirror line x = −b/(2a) through the vertex
roots	the x-values where y = 0; also called zeros or x-intercepts
y-intercept	where the curve crosses the y-axis; equals c for y = ax² + bx + c
discriminant	the value b² − 4ac that tells how many real roots a quadratic has
coefficient	the numbers a, b and c multiplying the terms of the quadratic
repeated root	a single root counted twice, where the parabola just touches the x-axis

🔒

You have read the summary. The board-ready model answers, grammar notes, one-touch audio and writing practice for this chapter are part of Lipi©.

See it, understand it, hear it read aloud, then write the exam answer with confidence, for a fraction of a tutor cost.