Question

Create your own unique quadratic equation in the form y = ax2 + bx + c. Use complete sentences and show all work to determine the following:

Does the graph open up or down? How do you know?
Explain whether the graph has a maximum or minimum point.
Find the vertex and x-intercepts of the graph.
@johnweldon1993

Answer 1

Alright...well this is relatively easy....have you come up with an equation??

Answer 2

Just come up with any random one...whatever decides to pop in your head lol

Answer 3

Uh, okay >.< y= 6x^2 + 4x +2

Answer 4

lol good....good random one :D haha

Okay so

1) Does the graph open up or down? How do we know?

For this...we would look at 'a' the leading coefficient that is in front if the x²

so we are looking at 6 here

\[y= {\color {blue}6}x^2 + 4x +2\]

If this....was -6.....we would have a parabola that opens downwards....
But...since this is 6....we have a parabola that opens Upwards

Answer 5

*So general rule for that...

in the equation

y = ax² + bx + c

if 'a' is POSITIVE we have a parabola that opens up
if 'a' is NEGATIVE we have a parabola that opens down

Get that part?

Answer 6

Yep!

Answer 7

Okay...part 2

2) Explain whether the graph has a maximum or minimum point.

Well for this...we would again look if the graph opens UP....or DOWN

if it opens up...we have something like



and if it opens down...we have something like