Quadratic functions

Graphs and Equations of Quadratic Functions I

Submitted by robert.marik on Sun, 11/25/2018 - 08:22

Quadratic functions and vertices of parabolas I

Submitted by robert.marik on Thu, 11/08/2018 - 10:57

Question:

For each quadratic function choose the vertex of the parabola.

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Level:

We should fence the land in a shape of an equilateral triangle. Choose the function that describes the dependence of the fenced land area

S

(in square meters) on the length

d

(in meters) of the fence used.

S = \frac{\sqrt{3}}{36} d^{2}

S = \frac{\sqrt{3}}{18} d^{2}

S = \frac{\sqrt{3}}{4} d^{2}

S = \frac{1}{36} d^{2}

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Level:

On a spool of mass

0.5 kg

is winded an aluminium wire of length

100 m

. Choose the function that describes the dependence of a mass of the spool with the wire

m

(in kilograms) on a diameter of the wire

d

(in millimetres). Wire density is

2 700 \frac{k g}{m^{3}}

Hint: The density of an object is defined as the ratio of the mass and the volume of the object.

m = \frac{27 π}{400} d^{2} + 0.5

m = 67500 π d^{2} + 0.5

m = \frac{27 π}{400} d^{2} - 0.5

m = \frac{27 π}{200} d^{2} + 0.5

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Level:

In the centre of a square shaped square there is a water fountain. The fountain has a square ground plan with the side length

4.5 m

. The square should be paved with cobblestones of size

25 cm \times 25 cm

. Choose the function that describes the dependence of the number of cobblestones needed (

n

) on the length of the square (

a

) given in meters.

n = 16 a^{2} - 324

n = \frac{a^{2}}{625} - 324

n = 16 a^{2} - 625

n = \frac{a^{2}}{16} - 324

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Level:

The annulus shaped component parts are punched from sheet metal. Diameter of the circular hole is

25 %

of the diameter of the whole component part. Choose the function that describes the dependence of the area (

S

) of material used to produce one component part on its outside diameter (

d

S = \frac{15}{64} π d^{2}

S = \frac{3}{8} π d^{2}

S = \frac{15}{32} π d^{2}

S = \frac{31}{64} π d^{2}

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Level:

We want to plant flowers into rectangular flower bed with longer side by one meter longer than its shorter side. Each flower needs

1 {dm}^{2}

of free space. From the following functions, choose the one that describes the dependence of the number of planted flowers

n

on the length

a

of the shorter side of the flower bed. (Assume that the dimensions of the flower bed are given in whole meters.)

n = (a^{2} + a) \cdot 100

n = (a^{2} + a) \cdot \frac{1}{100}

n = (a + 1)^{2} \cdot 100

n = (a^{2} + a)

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Level:

Suppose we want to paint a cube so that there remains an unpainted stripe along all the edges on each face. The width of the stripe should be

1 cm

. The producer gives the paint consumption

100 ml / 1 m^{2}

. From the following functions choose the one that describes the dependence of the paint consumption

V

on the length of the cube edge

a

. The paint consumption

V

is given in millilitres and the length of the cube edge

a

is given in meters.

V = {(a - \frac{1}{50})}^{2} \cdot 600

V = {(a - \frac{1}{50})}^{2} \cdot \frac{3}{50}

V = {(a - \frac{1}{100})}^{2} \cdot 600

V = (a - 2)^{2} \cdot 100

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Level:

There are graphs of three quadratic functions in the picture. Choose the formula which corresponds to all three functions graphed in the picture.

y = - (x + a)^{2} + 3

a \in (- \infty; 0]

y = - (x + a)^{2} + 3

a \in R^{+}

y = - (x + 3)^{2} + a

a \in R^{+}

y = - (x - 3)^{2} + a

a \in R^{+}

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Level:

There are graphs of three quadratic functions in the picture. Choose the formula which corresponds to all three functions graphed in the picture. Suppose that

a \in R^{+}

y = a (x + 2)^{2} - 1

y = a (x - 2)^{2} - 1

y = a (x - 1)^{2} + 2

y = 2 (x - a)^{2} + 1

Graphs and Equations of Quadratic Functions I