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Mixed exercises: Quadratic functions

Berechne für folgende Parabel die Scheitelpunktform und den Scheitelpunkt. Zeichne den Graphen.

$f (x) = x^{2} + 2 x + 5$

For this task you need the following basic knowledge: Scheitelpunkt einer Parabel
$f (x)$ $=$ $x^{2} + 2 x + 5$
↓
Quadratische Ergänzung.
$=$ $x^{2} + 2 x + {(\frac{2}{2})}^{2} - {(\frac{2}{2})}^{2} + 5$
↓
In eine Binomische Formel umschreiben
$=$ ${(x + 1)}^{2} - {(\frac{2}{2})}^{2} + 5$
$=$ ${(x + 1)}^{2} - 1 + 5$
$=$ ${(x + 1)}^{2} + 4$
$\to$ Scheitelpunkt: $S (- 1 ∣ 4)$
$f (x) = x^{2} + 4 x + 1$

For this task you need the following basic knowledge: Scheitelform einer Parabel
$f (x)$ $=$ $x^{2} + 4 x + 1$
↓
Quadratische Ergänzung.
$=$ $x^{2} + 4 x + {(\frac{4}{2})}^{2} - {(\frac{4}{2})}^{2} + 1$
↓
In eine Binomische Formel umschreiben.
$=$ ${(x + \frac{4}{2})}^{2} - {(\frac{4}{2})}^{2} + 1$
$=$ ${(x + 2)}^{2} - 2^{2} + 1$
$=$ ${(x + 2)}^{2} - 4 + 1$
$=$ ${(x + 2)}^{2} - 3$
↓
Scheitelpunkt ablesen
$\to$ Scheitelpunkt: $S (- 2 ∣ - 3)$
$f (x) = x^{2} - 4 x + 1$

For this task you need the following basic knowledge: Scheitelform einer Parabel
$f (x)$ $=$ $x^{2} - 4 x + 1$
↓
Quadratische Ergänzung.
$=$ $x^{2} - 4 x + {(\frac{4}{2})}^{2} + 1$
↓
In eine Binomische Formel umschreiben.
$=$ ${(x - \frac{4}{2})}^{2} - {(\frac{4}{2})}^{2} + 1$
$=$ ${(x - 2)}^{2} - 2^{2} + 1$
$=$ ${(x - 2)}^{2} - 4 + 1$
$=$ ${(x - 2)}^{2} - 3$
↓
Scheitelpunkt ablesen.
$\to$ Scheitelpunkt: $S (2 ∣ - 3)$

$f (x) = x^{2} - 3 x + 3,5$

$f (x) = x^{2} + x - 3$

$f (x) = - x^{2} + 2 x + 1$

$f (x) = - x^{2} + 5 x - 5$

$f (x) = \frac{1}{2} x^{2} + x + 2$

$f (x) = - \frac{3}{4} x^{2} + \frac{2}{3} x - \frac{1}{6}$

$f (x) = \frac{1}{3} x^{2} - \frac{2}{3} x + \frac{5}{3}$

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