How do you write an equation for an absolute value with a vertex?

f (x) = – | x + 2| + 3 In general, the graph of the absolute value function f (x) = a| x – h| + k is a “V” with vertex (h, k), slope m = a on the right side of the vertex (x > h) and slope m = – a on the left side of the vertex (x < h).

How do you tell if an absolute value function opens up or down?

For absolute value equations multiplied by a constant (for example,y=a| x |),if 01, it is stretched. Also, if a is negative, then the graph opens downward, instead of upwards as usual.

How do you find the axis of symmetry of an absolute value function?

Linear “pieces” will appear in the equation of the absolute value function in the following manner: y = | mx + b | + c where the vertex is (-b/m, c) and the axis of symmetry is x = -b/m. Note that the slope of the linear “pieces” are +1 on the right side and -1 on the left side.

How do you write an absolute value?

The most common way to represent the absolute value of a number or expression is to surround it with the absolute value symbol: two vertical straight lines.

1. |6| = 6 means “the absolute value of 6 is 6.”
2. |–6| = 6 means “the absolute value of –6 is 6.”
3. |–2 – x| means “the absolute value of the expression –2 minus x.”

What is an example of a absolute value function?

An absolute value equation is an equation in which the unknown variable appears in absolute value bars. For example, |x|=4,|2x−1|=3,|5x+2|−4=9.

What does the absolute value function do?

The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Algebraically, for whatever the input value is, the output is the value without regard to sign. Describe all values x within or including a distance of 4 from the number 5.

Do absolute value functions have symmetry?

An absolute value graph is symmetrical, meaning it can be folded in half on its line of symmetry. The function \begin{align*}y=|x|\end{align*} is the parent function, or most basic function, of absolute value functions.

What is the axis of symmetry function?

The axis of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves. The axis of symmetry always passes through the vertex of the parabola . For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .

What is the vertex of the absolute value function defined by?

CCSS.Math: HSF.IF.C.7. , HSF.IF.C.7b. The general form of an absolute value function is f(x)=a|x-h|+k.

How do you graph the absolute value function?

To graph an absolute-value function, choose several values of x and generate some ordered pairs. Have students substitute in x values (inputs) into the equation and solve for the y values (outputs). Then plot the points and draw the graph. Absolute-value graphs are shaped like the letter “V”.

How do you find the vertex of an absolute value equation?

Because the vertex has coordinates at the values that are being added/subtracted to the equation, the general form of an absolute value equation is y=|x-h|+k where vertex=(h,k).

What is an example of absolute value function?

A real world example of an absolute value function is any calculation in which the total depends upon simple addition of all the quantities in the function, regardless of sign. One example of such a calculation is the number of feet traveled by an athlete running around a race track.

What is absolute value function?

The absolute value function is commonly used to measure distances between points.