Standard Form of a Parabola Equation
This week in math we learned about the standard form of a parabola equation.
When using the standard form of the equation it is very useful because it reveals a lot about how to graph the equation without a table of values.
First of all, standard equation is: y = a
At first glance, it looks very confusing but with the information we have you are able to found out the directions opening, vertex, axis of symmetry, intercepts, domain, and range. Some information is found easily by just looking at the values that correspond with the variables but in some cases, the information you will have to be pieced together.
When looking at y = a
A, whether the parabola opens up or down and if the vertex is a maximum or minimum vertex. If the value of a is negative than the parabola opens down and we know the vertex will be at its maximum. If the value is positive then we know the parabola opens up and the vertex will be at its minimum.
P, tells you the horizontal translation. Also known as to when starting at 0 on the x-axis if you will be sliding left or right. Another thing to note is if the p-value follows a positive you will be sliding to the left (negative) by that many intervals and if the p-value follows a negative you will be sliding to the right (positive) by that many intervals. It will always be the opposite value.
Q, tells you the vertical translation. Also known as to whether you’ll be going up or down from the horizontal translation. If the q-value is negative you will be moving down by the amount of q and if the q-value is positive you will be moving up by the amount of q.
Now using this information we can piece it together to find the vertex, axis of symmetry, intercepts, domain, and range.
Taking our horizontal and vertical translations we can determine the vertex. The p-value will be the value of the vertex and the q-value will be our y-value of our vertex. Now that we have our vertex we now know our axis of symmetry. Our line of symmetry is just the horizontal translation or our x-value of the vertex. The axis of symmetry is the line that splits the parabola symmetrically in half.
Our domain will always be x = all real numbers and our range will be y >/= or </= to the y value of our vertex. So, if the vertex is at its minimum then y >/= (y vertex value). And if the vertex is at its maximum then y </= (y vertex value). In this case above y >/= 3.