What is the order, from narrowest to widest graph, of the quadratic functions f(x) = -10x2, f(x) = 2x2, f(x) = 0.5x2?
in y = ax^2
as |a| get bigger, the parabola become more narrow, and conversely,
as |a| gets smaller, the parabola becomes more open or wide.
so in your case, y = -10x^2 is the most narrow, the negative merely
shows that the parabola opens downwards
Well, let me illustrate it to you with a little light-heartedness. Imagine these quadratic functions are at a party.
First off, we have f(x) = -10x^2. This function is like a party pooper, with a negative leading coefficient that makes the parabola point downwards. So it's the narrowest of the bunch, kind of like trying to do the limbo under a really low bar.
Next up, we have f(x) = 2x^2. This function is a bit more outgoing, with a positive leading coefficient that makes the parabola curve upwards. So it's wider than our previous function, but still not as wide as it could be. It's like someone who's just slightly awkward at the party, trying to fit in.
Lastly, we have f(x) = 0.5x^2. This function is the life of the party, with a positive leading coefficient that makes the parabola open up even more. It's the widest of them all, like that person who takes up half the dance floor with their extravagant moves.
So, the order from narrowest to widest graph would be f(x) = -10x^2, f(x) = 2x^2, and f(x) = 0.5x^2. Let the quadratic party begin!
To determine the order of the quadratic functions from narrowest to widest graph, we need to compare the values of the coefficient in front of the x^2 term in each function.
The quadratic functions are:
1. f(x) = -10x^2
2. f(x) = 2x^2
3. f(x) = 0.5x^2
Comparing the coefficients, we can see that the coefficients in increasing order are:
-10, 0.5, 2
To determine the order of the functions, we need to arrange them in ascending order based on the coefficient values.
So, the order of the quadratic functions from narrowest to widest graph is:
1. f(x) = -10x^2
2. f(x) = 0.5x^2
3. f(x) = 2x^2
To determine the order of the quadratic functions from narrowest to widest graph, we need to compare the coefficients of the quadratic terms, which is the x^2 term.
The quadratic functions are:
1) f(x) = -10x^2
2) f(x) = 2x^2
3) f(x) = 0.5x^2
Comparing the coefficients of x^2, we can see that:
-10 < 2 < 0.5
Therefore, the order of the quadratic functions from narrowest to widest graph is:
1) f(x) = -10x^2
2) f(x) = 2x^2
3) f(x) = 0.5x^2