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The graphs of quadratic functions are parabolas; they tend to look like a smile or a frown. The points on a graph represent possible solutions to the equation based on high and low points on the parabola. The minimum and maximum points can be used in tandem with known numbers and variables to average the other points on the graph into one solution for each missing variable in the above formula. Quadratic functions can be highly useful when trying to solve any number of problems involving measurements or quantities with unknown variables. One example would be if you were a rancher with a limited length of fencing and you wanted to fence in two equal-sized sections creating the largest square footage possible. You would use a quadratic equation to plot the longest and shortest of the two different sizes of fence sections and use the median number from those points on a graph to determine the appropriate length for each of the missing variables.

The graph of a quadratic function is a curve called a parabola. Parabolas may open upward or downward and vary in "width" or "steepness", but they all have the same basic "U" shape. The picture below shows three graphs, and they are all parabolas. All parabolas are symmetric with respect to a line called the axis of symmetry. A parabola intersects its axis of symmetry at a point called the vertex of the parabola. You know that two points determine a line.

Graphs. A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero. The graph of a quadratic function is a.
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In algebra , a quadratic function , a quadratic polynomial , a polynomial of degree 2 , or simply a quadratic , is a polynomial function with one or more variables in which the highest-degree term is of the second degree. For example, a quadratic function in three variables x , y, and z contains exclusively terms x 2 , y 2 , z 2 , xy , xz , yz , x , y , z , and a constant:. A univariate single-variable quadratic function has the form . The graph of a univariate quadratic function is a parabola whose axis of symmetry is parallel to the y -axis, as shown at right. If the quadratic function is set equal to zero, then the result is a quadratic equation. The solutions to the univariate equation are called the roots of the univariate function.

The graph of a quadratic function is a parabola , a type of 2 -dimensional curve. The function of the coefficient a in the general equation is to make the parabola "wider" or "skinnier", or to turn it upside down if negative :. If the coefficient of x 2 is positive, the parabola opens up; otherwise it opens down. The vertex of a parabola is the point at the bottom of the " U " shape or the top, if the parabola opens downward. In this equation, the vertex of the parabola is the point h , k. So, the x -coordinate of the vertex is:.

The quadratic function has the form:. Note that if c were zero, the function would be linear. An advantage of this notation is that it can easily be generalized by adding more terms. We could for example write equations such as. In many books quadratic equations are written as.

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## What is a Quadratic Function?

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1. Piposade says:
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3. Thibaut R. says: