# Writing absolute value equations given a graph

Understand patterns, relations, and functions Relate and compare different forms of representation for a relationship; Represent and analyze mathematical situations and structures using algebraic symbols develop an initial conceptual understanding of different uses of variables; explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope; use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships; recognize and generate equivalent forms for simple algebraic expressions and solve linear equations Common Core State Standards CCSS 8. Determine the rate of change and initial value of the function from a description of a relationship or from two x, y values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. BACK The only absolute thing in this world is absolute value. Naturally, if absolute values are absolute, then so are absolute value functions. Know what else is absolute? Or at least the formation that geese fly in.

They conveniently always fly in a V shape. Who knew geese knew such advanced math? It looks exactly the same as the piecewise function that we talked about in the last unit.

In this piecewise function, f x is positive when x is negative, and f x is positive when x is positive. For us to meet here again, it must be fate; that, or mathematics.

Like play a smashing song on their lutes. Something particular to sink our teeth into and leave a mark on the page. Hopefully not a snake or a clown. Now we can make our graph. The two halves of the graph come to a point at 0, 0.

This is called the vertex of the absolute value function. The whole world turns on the vertex…or at least the whole function does.

If we find a point on one half of the graph, we can use it to find its twin on the other half. The negative sign outside of the absolute value bars flipped the whole graph upside down.

The 2 outside then made the V-shape narrower, making it easier to store in our closet. A number less than 1 would have an opposite effect, widening the graph and taking up all our closet space.

Ouch, did we just bump into the coffee table? Wait, we think that was a table of values we bumped into. With the lights on, we can graph this function.

In general, numbers added or subtracted outside the bars move the graph up or down. Numbers added or subtracted inside the bars should order a soda if they plan on driving. They also cause the graph to move left and right, but in the opposite direction of their sign. The equation for an absolute value function has the general form: The vertex of the graph is at h, k.

The graph is V-shaped. We can find the vertex at a glance, we know which way the graph points, and we can use symmetry to find two points for the effort of finding one.The most significant feature of the absolute value graph is the corner point at which the graph changes direction.

This point is shown at the origin in Figure \(\PageIndex{3}\). Figure \(\PageIndex{3}\): Graph of an absolute function.

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Engaging math & science practice! Improve your skills with free problems in 'Writing Basic Absolute Value Equations Given the Graph' and thousands of . - Shifting, Reflecting, and Stretching Graphs Definitions Abscissa The x-coordinate Ordinate The y-coordinate Shift A translation in which the size and shape of a graph of a function is not changed, but the location of the graph is.

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## Solving an Absolute Value Equation with Two Unknown Variables

To start practicing, just click on any link. L.2 Graph solutions to absolute value equations; L.3 Solve absolute value inequalities; L.4 Graph solutions to. Mrs. Jamison's Website. Search this site. Helpful Websites.

Math Dictionary. Geometry Reference. Free Algebra Worksheets. Solve Absolute Value Equations & Inequalities Video: Finding an Exponential Function Given its Graph.

Solving Inequalities in One Variable