How to I graph a quadratic equation?

Question

Pick the letter that cordspondes with each #.
1) y=2x²
2)x²
3) -1/3x²
_________
consider the shape of a parabola to be a "bowl". If the bowl is face up, then we say the "curve" is concave up. In respect to your equations, the standard form of the equation

y=ax^2 +b

"a" tells you if the curve is concave up or down ( pos or neg)
"b" tells you where it crosses the y axis when x is 0

My problems don't make sense, im given 8 equations and a empty graph that show parabala with out any x or y unit boxes.
Problems:
1) y=2x²
2)x²
3) -1/3x²

#3) is telling my that this parabala will be fat in a negative parabala, but there are like 4 negative parabala that shows the same thing. How do I know which is the right one?, they all look the same.

#1) would be skinny and postive parabala curve. There are 4 other postive parabala, how do I know to pick a right one?

Please, explain/show work.

Answer 1

Hi,

1) y = 2x² would open up from its vertex at (0,0). Because "a" = 2, the graph goes up 2 one square to each side of the vertex, so (-1,2) and (1,2) are 2 points on this graph.

2) y = x² would also open up from its vertex at (0,0). Because "a" = 1, the graph goes up 1 one square to each side of the vertex, so (-1,1) and (1,1) are 2 points on this graph.

Because "a" is bigger in y = 2x², this graph is narrower ans steeper than the graph of y = x².

3) y = -1/3x² would open down from its vertex at (0,0). Because "a" = -1/3, the graph goes down 1/3 of one square to each side of the vertex, so (-1,-1/3) and (1,-1/3) are 2 points on this graph. In addition if you wanted integer values, if x = 3 or -3, then y = -3. So (3,-3) and (-3,-3) are 2 more points on the line. To determine which of 4 graphs is correct, find other points like we did to see which has the correct values.

I hope that helps!! :-)

Answer 2

You have to scale the graph paper for each PARABOLA. For example, in #1, you may want to show the graph for y=-5 to y= 40 and x= -3 to x=3. You seem to know the concavity criteria (sign of the squared term). Also, PARABOLAs are symmetric about their minimum (or maximum) point. This helps you graph faster.