# A Cartesian framework

1. In a Cartesian framework, the functions f and g we know that:

the function (f) is defined by f (x) = 2x

1.1 write the coordinates of points (A) and (B)

1.2. indicate the solutions of the equation f (x) = g (x)

1.3. determine the area of the triangle [OAC]

2.1. In the figure, part of the graph of a quadratic function (f) of the type: f (x) = ax

point (O) is the origin of the reference, point (B) is the point of intersection of the graph of the function (g) with the ordinate axis equal to 6, point A is the point of the intersection of the graphs of the functions (f) and (g)

point (C) belongs to the abscissa axis and has abscissa equal to 4, the trapezium area [OBAC] is equal to 18

2.1 Determine the coordinates of the point (A)

2.2. Determine the algebraic expressions of the functions (f) (g)

the function (f) is defined by f (x) = 2x

^{2}, the function (g) is defined by g (x) = x + 3, the point (O) is the origin of the reference, point (C) is the point of intersection of the graph of the function (g) with the ordinate axis, points A and B are the points of intersection of the graphs of the functions (f) and (g)1.1 write the coordinates of points (A) and (B)

1.2. indicate the solutions of the equation f (x) = g (x)

1.3. determine the area of the triangle [OAC]

2.1. In the figure, part of the graph of a quadratic function (f) of the type: f (x) = ax

^{2}, a related function (g) and the trapezium [OBAC] are represented in a Cartesian framework. :point (O) is the origin of the reference, point (B) is the point of intersection of the graph of the function (g) with the ordinate axis equal to 6, point A is the point of the intersection of the graphs of the functions (f) and (g)

point (C) belongs to the abscissa axis and has abscissa equal to 4, the trapezium area [OBAC] is equal to 18

2.1 Determine the coordinates of the point (A)

2.2. Determine the algebraic expressions of the functions (f) (g)

### Correct answer:

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#### You need to know the following knowledge to solve this word math problem:

**geometry**- analytic geometry
**algebra**- quadratic equation
- equation
**arithmetic**- absolute value
**planimetrics**- Pythagorean theorem
- right triangle
- area of a shape
- triangle
- Heron's formula

#### Units of physical quantities:

#### Grade of the word problem:

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