## dietrich_harmon 2 years ago Order the group of quadratic functions from widest to narrowest graph.

1. terenzreignz

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

2. dietrich_harmon

3. dietrich_harmon

WHAT

4. terenzreignz

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.

5. dietrich_harmon

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...

6. terenzreignz

Yeah, that. :)