# How to Shrink a Parabola Vertically ... Comstock/Comstock/Getty Images

A parabola is the graphic representation of a quadratic equation. The constant multipliers, or coefficients, in a quadratic equation determine the way a parabola looks when you graph it on the x-y plane. You can alter parabolic graphs by adjusting the constants in the equation. If you multiply the entire quadratic equation by a number, you can vertically shrink and stretch the parabola.

## 1Vertical Shrinking and Stretching

In order to vertically shrink a function, you must multiply the entire function by a number between zero and one. This compresses the function; its y-values change slower than they did prior to the transformation. In the case of a quadratic equation, the parabola appears to widen across the coordinate plane. Conversely, if you wish to vertically stretch a function, you must multiply the entire function by a number greater than one. The function's y-values then change faster than they did prior to the transformation.

## 2Shrinking a Parabola

When you vertically shrink a parabola, the x-intercepts of the parabola do not change; the parabola will still intersect the x-axis at the same values that it did prior to the shrinking. However, the value of the vertex does change. Consider the parabola represented by the equation y=x^2+2x-3. In this equation, the x-intercepts are 1 and -3. If you input 2 for x, the resulting y-value is 5. If you multiply the whole equation by 1/2, it becomes y=(1/2)x^2 + x - 3/2. The x-intercepts are still 1 and -3. However, if you input 2 for x, the resulting y-value is 5/2. The function's y-values change at a slower rate; the parabola has been vertically shrunk.