Question

You and your friend need to graph quadratic functions of the form y =ax^2 and y =ax^2 + c. Your friend asks you to write some hints to help her graph these types of equations.
a. Explain the role of a.

b. Explain the maximum and minimum.

c. What is the vertex?

d. Explain the role of c.

Answer 1

C is how much the graph is moved up or down
A is how wide the graph opens up. Large A = small opening and vice versa
The vertex is when the graph changes direction
The maximum or minimum is the vertex depending on which way the parabola opens. if it opens up, its a minimum and opens down its a maximum

Answer 2

y =ax^2 is a parabola with its vertex at (0,0)
if a is positive, the parabola opens upwards and (0,0) is the minimum point of the parabola,
if a is negative, the parabola opens downwards and (0,0) is the maximum point of the parabola.
The constant c causes a vertical shift of y= ax^2 , if c is positive, it moves up, if c is negative, it moves down

e.g.
https://www.wolframalpha.com/input/?i=plot+y+%3D+2x%5E2+,+y+%3D+-2x%5E2,+y+%3D+2x%5E2+%2B+4,+y+%3D+2x%5E2+-+1

Answer 3

After reading Reiny's and Anonymous' response, all I can say is Excellent! Excellent! Those two paragraphs are load with good information on the parabola.