Foundation and Higher · quadratic graphs

Roots, intercept,
turning point.
Read them off.

three features,
one curve

the shape of every quadratic —

Parabola

y = x² − 2x − 3

a smooth, symmetrical curve

feature 1 of 3

The roots

1. Roots: where it crosses the x-axis.

2. On the x-axis, y = 0.

✓ Roots: x = −1 and x = 3

feature 2 of 3

The y-intercept

1. Where the curve crosses the y-axis.

2. There, x = 0, so y = 0 − 0 − 3.

✓ y-intercept: (0, −3)

feature 3 of 3

The turning point

1. The curve is symmetrical.

2. Halfway between the roots: x = 1.

3. y = 1² − 2 × 1 − 3 = −4.

✓ Turning point (1, −4): a minimum

without the graph

From the equation

1. Roots: put y = 0 and solve.

2. Intercept: put x = 0.

✓ Then sketch: mark all three features

y = x² − 2x − 3

0 = (x + 1)(x − 3) roots

x = −1 or x = 3

x = 0: y = −3 intercept

on any quadratic graph —

Roots

where y = 0

y-intercept

where x = 0

Turning point

halfway between the roots

Negative x²? The curve flips:
the turning point is a maximum.

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