Before starting this section, it is recommended you have atleast basic
understanding of Exponents & roots, polynomials, solve for x using factoring, and using the quadratic formula.
What is a coordinate or cartesian plane?
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What is a coordinate or cartesian plane?
Coordinate or cartesian plane is the backbone of function,
to truly understand functions, one needs to know and understand cartesian plane first.
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Introduction to functions
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Introduction to functions
Introduction to functions (linear, quadratic or parabola, and hyperbolar).
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Linear functions
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Linear functions
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The two points below, are found in a straight line. Find the gradient or slope of the line.
(0;0), (0; 0)
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Chances: 3
You get three chances for this question.
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Now, find the equation of the line
(0; 0)
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Chances: 3
You get three chances for this question.
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Find the y-intercept
(0;0), (0; 0)
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Chances: 2
You get two chances for this question.
The first question you got 0/3
The second question you got 0/3
The third question you got 0/2
Your total is therefore, 6/8.
Percentage
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Quadratic functions
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Visual introduction to parabolas
That is, what is a y-intercept, x-intercept and turning point or vertex.
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Graphing parabola or quadratic function part 1
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Graphing parabola or quadratic function part 1
There's a lot of approaches one can take to graphing, this video demonstrates one of the most recommended approaches which involves finding y-intercept, x-intercept, and turning point sometimes refered to as vertex.
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Graphing parabola or quadratic function part 2
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Graphing parabola or quadratic function part 2
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Working with parabolas or quadratic functions: Given the equation, f(x) = x2 + 6x + 5
Firstly, find the y-intercept.
The y intercept is a poing where the function touches the y-axis of the coordinate or cartesian plane, therefore the value of x is 0.
Hence, to find y-intercept , you simply put zero where there is x in the given equation.
Making the number without x (C) in the equation always the y-intercept.
y = x2 + 6x + 5
y = 02 + 6(0) + 5
y = 0 + 0 + 5
y = 5
Then, find the x-intercept or roots.
The x-intercept is a poing where the function touches the x-axis of the coordinate or cartesian plane, therefore the value of y is 0.
Hence, to find x-intercept , you simply put zero where there is y in the given equation and solve for x.
y = x2 + 6x + 5
0 = x2 + 6x + 5
0 = x2 + 5x + x + 5
0 = (x2 + 5x) (+ x + 5)
x(x + 5) 1(x + 5)
x + 1 = 0, x + 5 = 0
Therefore x = -1 or x = -5
If you still struggling with solve for x click the button below
Find the x-coordinate of the vertex by using x = -b/2a equation:
x = -b/2a
x = -(6)/2(1)
x = -6/2
x = -3
Then find the y-coordinate of the vertex by substituting x-coordinate in to the given equation:
y = (-3)2 + 6(-3) + 5
y = 9 - 18 + 5
y = - 9 + 5
y = -4
Therefore the vertex or turning point coordinates are (-3; -4)
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Given the quadratic function: f(x) = x200
Find the y-intercept.
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Chances: 2
You get a maximum of two chances for this question.
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Now, find the x- intercept/s of f(x) = x200.
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Chances: 3
You get a maximum of three chances for this question.
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f(x) = x200. Find the vertex or turning point coordinates.
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Chances: 3
You get a maximum of three chances for this question.
The first question you got 0/2
The second question you got 0/3
The third question you got 0/3
Your total is therefore, 0/8.
Percentage
%
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Introduction to hyperbola graphing
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Introduction to hyperbola
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Hyperbola
Hyperbolas have a general equation of
h(x) = a/(x + p) + q
.
In the general above, the sign of a determines the shape of the graph. If ais positive, e.g., h(x) = a/(x + p) + q, the graph of h(x) lies in the first and third quadrants.
And, if a is negative, e.g., h(x) = -a/(x + p) + q, the graph of h(x) lies in the second and forth quadrants.
p deals with horizontal shifts. When p value is positive, e.g., h(x) = a / (x + p) + q the graph shifts left, when P value is negative,e.g., h(x) = a / (x - p) + q the graph shifts right.
q on the other hand, deals with vertical shifts. When q value is positive, e.g., h(x) = a / (x + p) + q the graph shifts up, and when Q value is negative, e.g., h(x) = a / (x + p) - q the graph shifts down.
Asymptotes are determined by p and q values. q value is the horizontal asymptote, represented by y = q.
Equation is (-4/x) + 7. Therefore y = 7.
p value is the vertical asymptote, represented by x = -p.
Equation is 1/(x + 1). Therefore, x = -1.
Graph h(x) = 3/(x + 1) - 2
Asymptotes: y equals -2, x equals -1. Remember, asymptotes are lines, not points.
Shape: With a positive A value of 3, the graph has a top-right and bottom-left shape.
Intercepts:
Y-intercept: The graph contains intercepts the y-axis, when x = 0. Therefore, h(0) = 3/(0 + 1) -2
h(0) = (3/1) -2
h(0) = 3 - 2
h(0) = 1
Hence, y-intercept coordinates are (0, 1)
X-intercept: The graph intercepts the x-axis, when y = 0. Therefore, 0 = 3/(x + 1) -2
2 = 3/(x + 1)
Cross-multiply, 2(x + 1) = 3
2x + 2 = 3
2x = 3 - 2
2x = 1
x = 1/2
Hence, x-intercept coordinates are (1/2, 0)
Axis of Symmetry
The axis of symmetry intersects at the same point where the two asymptotes intersect.
Negative p and q value determine this point.
Calculating the axis of symmetry:
For positive slope: y = MX + C
Using the point (-1, -2) and gradient 1
-2 = 1(-1) + c
-2 = -1 + c
c = -1
Y-intercept for positive axis of symmetry: (0, -1)
For negative slope:
Using the point (-1, -2) and gradient -1
-2 = -1(-1) + c
-2 = 1 + c
-3 = c
Y-intercept for negative axis of symmetry: (0, -3)
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What is the y or horizontal asymptote and x or vertical asymptote of the following?
h(x)=(0/x0)0
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Chances: 2
You get a maximum of two chances for this question.
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Find the X-intercept of h.
Roundoff your answer into two decimal places
h(x)=(0/x0)0
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Chances: 3
You get a maximum of three chances for this question.
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Find the y-intercept of h.
Roundoff your answer into two decimal places
h(x)=(0/x0)0
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Chances: 3
You get a maximum of three chances for this question.
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Find axis of symmetry equations of h.
h(x)=(0/x0)0
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Chances: 4
You get a maximum of four chances for this question.
The first question you got 0/2
The second question you got 0/3
The third question you got 0/3
The forth question you got 0/4
Your total is therefore, 0/12.
Percentage
%
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Finding a Domain of any function
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Finding a Domain of any function
The domain of a function is the set of all possible x-values for the function.
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Solve the following: 0/0 x 0/0
Chances: 1
You get one chance for this question.
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Solve the following: 0/0 ÷ 0/0
Chances: 1
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Solve the following: 0/0 + (0)/0
Chances: 2
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Solve the following: 0/0 + 0/0
Chances: 2
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Solve the following: 0/0 - 0/0
Chances: 2
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A a box with a mass of 0kg rests on a flat surface, find the normal acting on the box.
Chances: 2
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Find the static friction of the box, if its coefficient was 0.
Chances: 2
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The box is now pushed horizontal to the right by a force of 0N is moving to the right with an acceleration of 0m/s2, what is the coefficient of the kinetic friction?
Chances: 3
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The box is now pushed at angle of 0° to the right by a force of 0N, Calculate the new normal force.
Chances: 3
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As the box continue to move, what is the acceleration of the box if kinetic friction coeffient was 0.
Chances: 3
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