a(x-p)^2+q

vertex=(p,q)

In this unit I learned how standard form quadratic functions can be interpreted from the equation y=a(x-p)²+q. The “a” value tells you the shape of the graph. The higher the magnitude of the “a” value, the more skinner the parabola becomes. The lower the magnitude of the “a” value, the wider the parabola becomes. If the “a” value is positive, then the graph opens up. If the “a” value is negative, the parabola opens down. The “p” value tells us the translation of the parabola to the right or the left. For example, if p=4, the graph would be translated 4 units to the right and the vertex would be 4 units to the right of the origin. The “q” value tells us the translation of the graph up or down. For example, if q=-8, the graph would be translated 8 units down and the vertex would be 8 units down of the origin.

Here is an example of how we can use this equation to interpret how the graph may look like.

We will use the equation y=0.5(x-8)²+64.

From this equation we know that a=0.5, p=8, ad q=64.

Since, a=0.5, we can interpret that every coordinate will be 0.5 multiplied by the regular coordinate of what it would be as x². We also know that the graph will be wider than x².

Since p=8, we can interpret that the graph will be translated 8 units to the right.

Since q=64, we can interpret that the graph will be translated 64 units up.