One of the things we learned this week in Precalc 11 is how the the parent function is transformed when dealing with different quadratic equations, by being able to see the graph, we can determine the equation.

Parent Function

The parent function has a pattern of 1-3-5…., which means it goes up 1, one to the right, goes up 3, one to the right, goes up 5, one to the right and it keeps on going, the same pattern also happens to the left.

When dealing with an equation that kind of looks like where , the parabola is either compressing (a<1) or stretching (a>1), if the value is negative the parabola is a reflection over the x-axis. or is the parent funtion. We can identify the coefficient by looking for the pattern at which it goes up by.

With an equation similar to where , the parabola translates vertically meaning it’s moving up or down depending if the a value is a positive or a negative number.

For equations like where , the parabola translates horizontally meaning it’s moving left or right depending if the a value is a positive or a negative number.

Examples

Equation

Since the parabola translated horizontally to the right, we know that the equation was and since it moved to the right we can assume that it’s subtracting.

Equation

the parabola translated vertically up so the equation was and since it moved up 9 times, we know that it’s adding 9.

Equation

The parabola didn’t translate vertically or horizontally, so we can assume that it compressed or stretched, it’s not opening down so a must be positive. If we find the pattern, it goes up by 3, then 9, so a must be 3.