A Cartesian framework
1. In a Cartesian framework, the functions f and g we know that:
the function (f) is defined by f (x) = 2x2, 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) = ax2, 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)
the function (f) is defined by f (x) = 2x2, 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) = ax2, 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:

Tips for related online calculators
Line slope calculator is helpful for basic calculations in analytic geometry. The coordinates of two points in the plane calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of the segment, intersections of the coordinate axes, etc.
Are you looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
Do you want to convert length units?
See also our trigonometric triangle calculator.
Are you looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have a quadratic equation?
See also our right triangle calculator.
Do you want to convert length units?
See also our trigonometric triangle calculator.
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:
Related math problems and questions:
- General line equations
In all examples, write the GENERAL EQUATION OF a line that is given in some way. A) the line is given parametrically: x = - 4 + 2p, y = 2 - 3p B) the line is given by the slope form: y = 3x - 1 C) the line is given by two points: A [3; -3], B [-5; 2] D) t
- Quadratic function
It is given a quadratic function y = -4x2+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.
- Intersections 49433
Draw a graph of the function given by the equation y = -2x +3, determine its intersections with the coordinate axes, and complete the missing coordinates A [3 ;? ], B [? ; 8].
- Curve and line
The equation of a curve C is y=2x² -8x+9, and the equation of a line L is x+ y=3 (1) Find the x coordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
- Circle
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: (x-x_S)2+(y-y_S)2=r2
- Intersection 74914
Find the perimeter of triangle ABC, where point A is the beginning of the coordinate system, and point B is the intersection of the graph of the linear function f: y = - 3/4• x + 3 with the x-axis, and C is the intersection of the graph of this function w
- Intersections 62784
A quadratic function is given: y = -x² + 2x + 3 a) determine the intersections with the x, y axis and peak V b) draw a graph and describe c) for which x applies f (x) = 3
- Points on circle
In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are
- Intersection of Q2 with line
The equation of a curve C is y=2x² - 8x +9, and the equation of a line L is x + y=3. (1) Find the x-coordinates of the points of intersection of L and C. (ii) show that one of these points is also the
- Parametric equation
Point A [6; -2]. Point B = [-3; 1] Write the parametric equation of the line BA so that t belongs to the closed interval < 0;3 >
- On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
- Parabola
Find the equation of a parabola that contains the points at A[6; -5], B[14; 9], C[23; 6]. (use y = ax2+bx+c)
- Intersection 8295
Write whether the function is ascending or descending and determine the coordinates of the intersection with the x and y axes: y = 3x-2 y = 5x + 5 y = -0.5x-1
- Coordinates 59863
The endpoint of the vector is given, which is located at the origin of the Cartesian system Oxy. Determine the coordinates of the vector, and its magnitude, and sketch it: P[3,4]; Q[-2,7]; S[-5,-2] . .. i.e., Vectors PO, QO, SO
- Vector - basic operations
There are given points A [-9; -2] B [2; 16] C [16; -2] and D [12; 18] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w
- Determine 46853
Determine the number an in the function y = ax-2 if its graph passes through point A (1, -4).
- Intersection 3486
There is a point A [-2; -4] in the rectangular coordinate system and a point S [0; -2]. Determine the coordinates of points B, C, and D so that ABCD is a square and S is the intersection of their diagonals.