In absolute value graphs, a dilation makes the V either wider or thinner. We accomplish this by putting a value in front of the absolute value (for example, y=2|x| or y=1/3|x|).

**SOLVING EQUATIONS CONTAINING ABSOLUTE VALUE(S)**

- Step 1: Isolate the absolute value expression.
- Step2: Set the quantity inside the absolute value notation equal to + and – the quantity on the other side of the equation.
- Step 3: Solve for the unknown in both equations.
- Step 4: Check your answer analytically or graphically.

what determines if a parabola is narrow or wide? The coefficient of the quadratic term, a, **determines** how **wide** or **narrow** the graphs are, and **whether** the graph turns upward or downward. A positive quadratic coefficient causes the ends of the **parabola** to point upward. The greater the quadratic coefficient, the **narrower** the **parabola**.

Also asked, how do you find the absolute value?

The **absolute value** of a number is the number’s distance from zero, which will always be a positive **value**. To **find** the **absolute value** of a number, drop the negative sign if there is one to make the number positive. For example, negative 4 would become 4.

What does the A mean in a parabola?

As we can see from the graphs, when 0 < |a| < 1 (|a| **means** absolute value of a), the **parabola** appears wider. When |a| > 1, the **parabola** appears thinner. When a is positive, the **parabola** opens upwards; when a is negative, the **parabola** opens downward.

### What determines the width of a parabola?

a determines the width and the direction of the parabola: The larger |a| becomes, the wider the parabola. If a is positive, the parabola opens upward, and if a is negative, the parabola opens downward.

### What are coefficients?

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression. For example, if y is considered as a parameter in the above expression, the coefficient of x is −3y, and the constant coefficient is 1.5 + y.