Maths important things 2.6 - test week 1

Standard form

f(x) = ax² + bx + c

Standard form: If a>0, the parabola opens…

…upwards; its vertex is the minimum turning point and the curve is concave up.

Standard form: If a<0, the parabola opens…

…downwards; the vertex is the maximum turning point and the curve is concave down.

Standard form: y-intercept of the parabola

(0,c)

Standard form: The vertex of the parabola is…

(-b/2a, f(-b/2a))

The axis of symmetry of the parabola is the vertical line…

-b/2a

Vertex form

f(x) = a(x-h)² + k

Vertex form: The vertex of the parabola is the point…

(h,k)

Vertex form: If a>0, the parabola is…

concave up

Vertex form: If a<0, the parabola is…

concave down

Vertex form: The axis of symmetry has equation…

x = h

Vertex form: The y-intercept is…

(0, ah² + k)

Factorised form

f(x) = a(x-p)(x-q)

Factorised form: The x-intercepts of the parabola are…

(p, 0) and (q, 0)

Factorised form: The y-intercepts of the parabola are…

(0, apq)

Factorised form: The axis of symmetry has equation…

x = p+q/2

Factorised form: The vertex of the parabola is…

(p+q/2, f(p+q/2)), where f(p+q/2) = −a(p−q)²/4