Quadratic Function
A quadratic function is a type of mathematical function that can be represented by an equation in the form of f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the variable
A quadratic function is a type of mathematical function that can be represented by an equation in the form of f(x) = ax^2 + bx + c, where a, b, and c are constants and x is the variable. Here, a cannot be zero as it determines the shape of the parabola.
The graph of a quadratic function is a U-shaped curve called a parabola. The vertex of the parabola represents the minimum or maximum point of the function, depending on whether the coefficient a is positive or negative, respectively.
Quadratic functions have several important properties, including the axis of symmetry, which is a vertical line that divides the parabola into two symmetrical halves. The equation for the axis of symmetry is x = -b/2a. The vertex of the parabola lies on the axis of symmetry.
The y-intercept of a quadratic function is the value of y when x is equal to zero, which is simply the constant term c in the equation. The x-intercepts, also called roots or zeros, are the values of x when y is equal to zero. These can be found by solving the quadratic equation ax^2 + bx + c = 0. The discriminant, b^2 – 4ac, can be used to determine the nature of the roots. If the discriminant is positive, there are two real and distinct roots. If it is zero, there is one real and repeated root. If it is negative, there are two complex conjugate roots.
Quadratic functions can be used to model various real-life situations, such as projectile motion, profit and revenue optimization, and finding the maximum or minimum value of a quantity.
To graph a quadratic function, you can use several methods, including finding the vertex and plotting key points, or by creating a table of values and connecting the dots.
I hope this explanation helps! If you have any further questions, feel free to ask.
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