Equation for Curved Lines in Algebra

Not all algebra graphs will be linear.
••• Hemera Technologies/Photos.com/Getty Images

Algebra students often have a difficult time understanding the relationship between a graph of a straight or a curved line and an equation. Because most algebra classes teach equations before graphs, it is not always clear that the equation describes the shape of the line. Therefore, curved lines are a special case in algebra; their equations may take on one of many forms, depending on the curved line you are dealing with.

Quadratic Equations

In high school algebra, the kinds of curved lines that students are most likely to see are the graphs of quadratic equations. These equations take the form of f(x) = ax^2 + bx + c, and can be solved a variety of ways; students will often be asked to find the solutions, or the zeros, of these graphs, which are the points at which the graph crosses the x-axis. Before working with the graphs, however, students should be comfortable with the format of quadratic equations and may work on factoring them as well.

Graphing Quadratic Equations

Quadratic equations will graph as parabolas, or symmetrical curved lines that take on a bowl-like shape. These equations will have one point that is higher or lower than the rest, which is called the vertex of the parabola; the equations may or may not cross the x or y axis.

Negative Lines

A parabola that is graphed downwards, or that looks like an upside-down bowl, has a negative coefficient for the part of the equation ax^2. In this case, the vertex will be the highest point on the parabola. However, the axis of symmetry, or the perfect symmetry present in parabolic/quadratic equations with positive coefficients, will remain the same.

Other Curved Lines

Students may come across curved lines that are not quadratic equations; these expressions may have some other kind of exponent attached to the variable, such as x^3 or even higher expressions. To find the equation for a non-parabolic, non-quadratic line, students can isolate points on the graph and plug them into the formula y = mx+b, in which m is the slope of the line and b is the y-intercept.

Related Articles

Algebra 1 Substitution Method
Facts About Functions for Algebra 1
How to Write an Absolute-Value Equation That Has Given...
How to Find X-Intercept & Y-Intercept
Algebra 1 Compared to Algebra 2
How to Graph Inequalities on a Number Line
How to Find the Inequalities From a Graph
What Is Precalculus?
How to Solve Binomial Equations by Factoring
How to Solve Special Systems in Algebra
What Should a 10th Grade Math Student Know?
How to Identify a Numerical Coefficient of a Term
What Is the Difference Between a Quadratic and a Linear...
How to Program a TI 83 Plus Calculator to Solve Rational...
How to Graph With Scientific Calculators
Linear Factors of Polynomials
How to Solve a Parabola
How to Find Slopes
How to Solve a Quadratic Equation With a Casio Calculator
How to Find the Coordinates of a Hole in a Graph

Dont Go!

We Have More Great Sciencing Articles!