Quadratic | Matematik | Noter for over 20 sider

Opgavebeskrivelse
Exercise 1

Exercise 1.1
We want to find out if the graph f1(x) = 3x +4 is a parabolic graph.

Exercise 1.2
We want to find out if the graph f2(x)=3x^(2)+2x+6 is a parabolic graph.

Exercise 1.3
We want to find out if the graph f3(x)=-4x^(2)+3 is a parabolic graph.

Exercise 1.4
We want to find out if the graph f4(x)=3x*x^(2)+3x+8 is a parabolic graph.

Exercise 1.5
We want to find out if the graph f5(x)= (x+3) (x-4) is a parabolic graph.

Exercise 1.6
We want to find out if the graph f6(x)=3x^(3) is a parabolic graph.

Exercise 1.7
We want to find out if the graph f7(x)=3ℯ^(2x)+2ℯ^(x)+4 is a parabolic graph.

Exercise 1.8
We want to find out if the graph f8(x) = 2x − 3 √ x + 4 is a parabolic graph.

Exercise 1.9
We want to find out if the graph f9(x) = 3 is a parabolic graph.

Exercise 2
Determine the largest domain and range of a function defined by:

Exercise 4

Exercise 4.1
Plot the graph of f1(x) = 3x2 + 2x + 6 the function in Geogebra. Determine, using the formula (xt , yt ) = (-b/2A , -D/4A) and Geogebra, the vertex points on the graph.

Exercise 4.2
Plot the graph of f2(x) = −3x2 + 2x + 6 the function in Geogebra. Determine, using the formula (xt , yt ) = (-b/2A , -D/4A) and Geogebra, the vertex points on the graph.

Exercise 4.3
Plot the graph of f3(x) = −4x2 + 3x − 5 the function in Geogebra. Determine, using the formula (xt , yt ) = (-b/2A , -D/4A) and Geogebra, the vertex points on the graph.

Exercise 4.4
We need to plot the graph in GeoGebra and determine the vertex points

Exercise 4.5
We need to plot the graph in GeoGebra and determine the vertex points.

Exercise 4.6
We need to plot the graph in GeoGebra and determine the vertex points.

Exercise 6
Determine the largest possible domain and range in a second order polynomial.

Exercise 7

Exercise 7.1
Determine the domain and range of this function and then print it in GeoGebra.

Exercise 7.2
Determine the domain and range of this function and then print it in GeoGebra.

Exercise 7.3
Determine the domain and range of this function and then print it in GeoGebra.

Exercise 8

Exercise 8.1
In this case we need to solve the following quadratic equation using theorem 3

Exercise 8.2
In this case we need to solve the following quadratic equation using theorem 3

Exercise 8.3
In this case we need to solve the following quadratic equation using theorem 3

Exercise 8.4
In this case we need to solve the following quadratic equation using theorem 3

Exercise 8.5
In this case we need to solve the following quadratic equation using theorem 3

Exercise 9

Exercise 9.1
In this case we need to solve the following quadratic equation using theorem 3

Uddrag
And we know that the parabola is a ‘’happy’’ one because A > 0 so then we know that the 5.66 is the ymin. Therefore, the domain and range will look like this.

Dm = [xmin ; xmax]
Dm = ] -∞ ; + ∞ [
Vm = [ymin ; ymax]
Vm = [ 5.66 ; + ∞ [

So as a conclusion the domain is Dm = ] -∞ ; + ∞ [ and the range is Vm = [ 5.66 ; + ∞ [

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We can see that we have to find ymax because A < 0 then we know that it is a ‘’sad’’ parabola. Therefore, we know that -4.44 is the ymax. Now we must use the formula (xt , yt ) = (-b/2A , -D/4A) to solve it.

f3(x) = −4x2 + 3x − 5

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