Maths important things 2.6 - test week 1

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Math

IB Mathematics: Analysis and Approaches (SL)

Functions

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17 Terms

1
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Standard form

f(x) = ax2 + bx + c

<p>f(x) = ax<sup>2</sup> + bx + c</p>
2
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Standard form: If a>0, the parabola opens…

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

<p>…upwards; its vertex is the <strong>minimum</strong> turning point and the curve is <strong>concave up</strong>.</p>
3
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Standard form: If a<0, the parabola opens…

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

<p>…downwards; the vertex is the <strong>maximum</strong> turning point and the curve is <strong>concave down</strong>.</p>
4
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Standard form: y-intercept of the parabola

(0,c)

5
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Standard form: The vertex of the parabola is…

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

<p>(-b/2a, f(-b/2a))</p>
6
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The axis of symmetry of the parabola is the vertical line…

-b/2a

<p>-b/2a</p>
7
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Vertex form

f(x) = a(x-h)2 + k

<p>f(x) = a(x-h)<sup>2 </sup>+ k</p>
8
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<p>Vertex form: <span>The </span><strong>vertex</strong><span> of the parabola is the point…</span></p>

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

(h,k)

9
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<p>Vertex form: If a&gt;0, <span>the parabola is…</span></p>

Vertex form: If a>0, the parabola is…

concave up

10
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<p>Vertex form: If a&lt;0, the parabola is…</p>

Vertex form: If a<0, the parabola is…

concave down

11
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<p>Vertex form: <span>The </span><strong>axis of symmetry</strong><span> has equation…</span></p>

Vertex form: The axis of symmetry has equation…

x = h

12
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Vertex form: The y-intercept is…

(0, ah2 + k)

<p>(0, ah<sup>2 </sup>+ k)</p>
13
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Factorised form

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

<p>f(x) = a(x-p)(x-q)</p>
14
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Factorised form: The x-intercepts of the parabola are…

(p, 0) and (q, 0)

15
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Factorised form: The y-intercepts of the parabola are…

(0, apq)

16
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Factorised form: The axis of symmetry has equation…

x = p+q/2

<p>x = p+q/2</p>
17
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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

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