Week 9 of pre-calculus 11 we went over the vertex form also known as standard form. This form is a type of quadratic and it gives us the vertex. Different parts of the vertex form tell you different things which is what I will be going over today.
This is how vertex form looks like:
Now that you know how it looks I will show you what each part does to the parabola.
REFLECTION (open up/down)– if there is a negative in front of the coefficient that means the parabola open downwards, if it is positive the parabola will open upwards
STRETCH (slim/wide) – if there is a coefficient this tells us if our parabola will be wider or skinnier (congruent in is something you get from this as well)
HORIZONTAL TRANSLATION (left/right) – if the number inside the bracket it’s negative it goes to the right, if you if the number in the bracket is positive then it goes to the left (opposites)
VERTICAL TRANSLATION (up/down) – The number is positive at the end it goes up, if the Number at the end is negative it goes down.
In this example we know that our parabola will be opening down and it will be slimmer. The parabola will move three to the right and seven up. So we know that the vertex will be (3,7)!
Questions:
– Why is it slimmer if there’s a number?
First need to know how our parent function looks like. A parent function is the original parabola before we start to change things.
Now in the example we did before it had a coefficient of three which means the partent function is multiplied by three.
