quadratic function
A quadratic function is a polynomial function of degree 2, which means that the highest power of the variable in the equation is 2
A quadratic function is a polynomial function of degree 2, which means that the highest power of the variable in the equation is 2. The general form of a quadratic function is given by:
f(x) = ax^2 + bx + c
In this equation, “a” is the coefficient of the quadratic term, “b” is the coefficient of the linear term, and “c” is the constant term.
The graph of a quadratic function is a U-shaped curve called a parabola. The vertex of the parabola is the lowest or highest point, depending on whether the coefficient “a” is positive or negative. The axis of symmetry is a vertical line that passes through the vertex, and it divides the parabola into two symmetrical halves.
To find the vertex of a quadratic function, you can use the formula:
x = -b / (2a)
y = f(x) = a(x^2) + bx + c
Substitute the value of “x” back into the equation to find the value of “y”. The vertex will have the coordinates (x, y).
You can also find the x-intercepts (also known as zeros or roots) of a quadratic function by setting the function equal to zero and finding the values of “x” that make the equation true. This can be done by factoring, using the quadratic formula, or completing the square.
Other important points on a quadratic function’s graph include the y-intercept, which is the point where the graph intersects the y-axis, given by the value of “c” in the equation, and the axis of symmetry, which is the vertical line that passes through the vertex.
It’s worth noting that the behavior of a quadratic function depends on the sign of the coefficient “a”. If “a” is positive, the parabola opens upwards, and if “a” is negative, the parabola opens downwards.
Quadratic functions have many applications in mathematics, physics, engineering, and other fields. They can be used to model various real-world phenomena, such as projectile motion, economic curves, and optimization problems.
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