Question

Order the group of quadratic functions from widest to narrowest graph.

Answer 1

All these quadratic functions, before you even show them, see that coefficient of the
x² ?
The smaller the coefficient, the wider the graph ;)

Answer 2

WHAT

Answer 3

Let me rephrase that
The smaller the absolute value of the coefficient of the x² part, the WIDER the graph.

For example
x² + 5x + 3
4x² -2x + 9

The first graph would be wider as the coefficient of x² there (1) is smaller than the coefficient of the x² in the second (4).

BE CAREFUL, I said ABSOLUTE VALUE. So if you had
x² + 5x + 3
-4x² +2x - 9
instead,
the first graph is still wider even though -4 < 1.
In other words, disregard the sign of the x², and the smaller the coefficient, the wider.

Answer 4

Short answer:
y=2x^2 is the widest
y=5x^2 is the narrowest


Long answer:
To solve, think about the numbers.
Say x = 0.
y=0 in all three problems then.

Okay, now say x=3.
y = 5x^2 = 5(3^2) = 45 *higher number "goes up faster" when graphed
y = 4x^2 = 4(3^2) = 36
y = 2x^2 = 2(3^2) = 18 *lower number make a "wider" graph

Basically, think about;
y = Ax^2
The bigger 'A' is, the slimmer the graph.


* if you want to get technical, no graph is "wider", since they all can reach to infinity & negative infinity in this case, but that's far outside the question...

Answer 5

Yeah, that. :)