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Quadratic Function & Inequalities - Coggle Diagram
Quadratic Function & Inequalities
General Formula
Express the quadratic equation in the standard form of ax + bx + c = 0
Substitute a, b and c into the general formula:
Solve for both values of x
Completing the Square
Express the quadratic equation in the form of a(x - h) - k = 0
Make (x-h)
the subject of the equation and solve for both values of x
Express the quadratic function in the form of y = a(x - h) + k
If a is positive, it will have a minimum point. If a is negative, it will have a maximum point.
The turning point is (h, k)
Factorization
Express the quadratic equation in the form of (x - a)(x - b) = 0
Either x - a = 0 or x - b = 0, so the roots of the equation are a and b
Express the quadratic function in the form of y = a(x - α)(x - β)
If a is positive, the graph has a minimum point. If a is negative, the graph has a maximum point
The x-intercepts are α and β
Substitute the x-coordinate of the turning point into the equation as x. Solve for the value of y to obtain the y-coordinate of the turning point.
The x-coordinate of the turning point is the average of α and β
Factorize the quadratic inequality to a(x - α)(x - β) > 0 or a(x - α)(x - β) < 0
Sketch out the curve and mark out the x-intercepts, α and β.
The part of the graph above the x-axis indicates y > 0. The part of the graph below the x-axis indicates y < 0.
Graphical
Re-express the quadratic equation such that the left-hand side is the expression for the quadratic graph.
Draw a line where the y-axis is the expression on the right-hand side of the equation
The solution to the equation is the point(s) of intersection of the two graphs