order the group of quadratic functions from Widest to Narrowest graph.
Y=7×^2, y= 1/4 x^2, Y =-2x^2
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https://www.wolframalpha.com/input/?i=plot+y%3D7x%5E2%2C+y%3D+1%2F4+x%5E2%2C+y+%3D-2x%5E2
To order the group of quadratic functions from widest to narrowest, we need to determine their widths based on the coefficients of their leading terms.
The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.
Let's compare the leading coefficients of the quadratic functions given:
1. y = 7x^2, which has a leading coefficient of 7.
2. y = (1/4)x^2, which has a leading coefficient of 1/4.
3. y = -2x^2, which has a leading coefficient of -2.
The wider the graph of the quadratic function, the larger the absolute value of the leading coefficient. Therefore, we can conclude that the order of widest to narrowest is as follows:
Widest: y = 7x^2 (leading coefficient = 7)
Middle: y = (1/4)x^2 (leading coefficient = 1/4)
Narrowest: y = -2x^2 (leading coefficient = -2)
So, the correct order from the widest to the narrowest graph is:
1. y = 7x^2
2. y = (1/4)x^2
3. y = -2x^2
consider the basic function y = x^2
y = 7x^2 = (√7 x)^2 has been scaled by a factor of 1/√7
y = 1/4 x^2 = (1/2 x)^2 has been scaled by a factor of 2
y = -2x^2 = -(√2 x)^2 has been scaled by a factor of 1/√2
So now just sort the scale factors
y=-1/4x^2,y=-2x^2,y=7x^2
this is the order from widest to narrowest graph
and if u want an explanation lmk
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