Today I’m learning something new but I don’t know how to solve this. I have 2 questions about it but I feel as if, if someone explain/ show how I can complete the first one I’ll be fine with doing the second one in my own.
How is a graph different from the parent function y=x^2 if you have:
A. |a| >1 in the equation y=ax^2
My teacher wants me to use Desmo (it’s a graphing calculator) it graphs things for you. But I don’t know if this will be a V like graph or a U like graph. Can someone help me so I can plug this in correctly please.
the 2nd order (square) means this is a parabola (more like a U)
the larger a is, the "flatter" the parabola will be
A bread company has a total of 12 packages of buns to sell. Each package of buns contains 6 buns and sells for $2.50. The cost of the buns, in dollars, is a function of the number of packages bought.
Which of the following values are in the domain of the function described? Select all that apply.
THanks you Scott is there a specific way I’m supposed to put it in the calculator?
To understand how the graph of the equation y = ax^2 is different from the parent function y = x^2 when |a| > 1, let's break it down step by step.
1. Start by considering the parent function y = x^2. This is a simple quadratic function that forms a symmetrical U-shaped graph, where the vertex (the lowest point) is located at the origin (0,0), and it opens upward.
2. When you introduce the absolute value of a in the equation y = ax^2, the graph can have two different shapes, depending on the value of a.
a) If a > 0: The graph will be similar to the parent function, a U-shaped graph that opens upward. The only difference is that the graph will become narrower or wider compared to the parent function as the absolute value of a increases. The vertex remains at the origin.
b) If a < 0: In this case, the graph will become an inverted U-shaped graph, commonly known as an upside-down U or a V-shaped graph. The vertex will still be at the origin, but the graph will open downward instead of upward.
To visualize these differences on Desmos, follow these steps:
1. Open the Desmos graphing calculator.
2. In the input box, type the equation "y = ax^2" and press Enter.
3. To get the graph corresponding to |a| > 1, replace "a" with a value greater than 1 or less than -1. For example, you can try substituting "a" with 2 or -2.
4. As you enter the modified equation, Desmos will automatically update the graph for you, allowing you to see the changes in real-time.
By observing the graph on Desmos, you'll be able to visualize how the graph of y = ax^2 differs from the parent function y = x^2 when |a| > 1. This will help you understand the shape and orientation of the graph. Once you're comfortable with this concept, you can apply the same understanding to solve the second question on your own.