This week, in precalc 11, I learned how to read and analyze quadratic functions. The standard form that we will be discussing is…
a$latex(x-p)^2$ +q)
With this standard form, we will be going over each part of the formula and discussing how it will effect our parabola.
Let’s start with “a”. This value will determine if our parabola will open up or down. “a” will also effect the stretch of our parabola. The higher the value, the more the parbola will stretch.
Let’s see what happens when the value of “a” is set to a positive number. As we can see when our “a” is set to a positive number, our parabola will open upwards.
Now let’s see what happens when the value of “a” is set to a negative number. As we can see when our “a” is set to a positive number, our parabola will open downwards.
Next, let’s cover “p”. So “p” will effect the vertex’s x position, but here’s the tricky part. It will move it in the opposite direction. So if we have -2 as our “p” value, the vertex will be +2 on the x axis. Let’s try it out. We can see that our “p” is -2 but out vertex’s x value is +2. This applies for postive numbers as well
Let’s take a look what happens if we have +2 in our “p”. We can see that our vertex shifted to -2.
“q” is also very similar to “p” except it moves it’s vertical positioning instead of horizontally.
For “q” the value is the real value that it will move up or down, for example +2 will move it 2 up on the y axis and -2 will move it down 2 on the y axis. As we can see when we put the “q” value as +2 it really moves it up by 2.
And when we set “q” as -2, it moves it down by 2.
