Given the graphs of the equations:
[tex]\begin{gathered} y=Ax^2 \\ y=Bx^2 \\ y=Cx^2 \\ y=Dx^2 \end{gathered}[/tex]
Where A, B, C, and D are Leading Coefficients.
You know that they are parabolas. Notice that the vertex of each parabola is at the Origin.
(a) By definition, when the Leading Coefficient is positive, the parabola opens upward, and when it is negative, the parabola opens downward.
Therefore:
- Since the first and the second parabola open downward, you can determine that the Leading Coefficients are negative.
- Since the third and the fourth parabola open upward, you can determine that the Leading Coefficients are positive.
(b) By definition, for a Quadratic Function in the form:
[tex]y=ax^2[/tex]
If:
[tex]|a|>1[/tex]
The parabola is streched.
If:
[tex]0<|a|<1[/tex]
The parabola is compressed.
Therefore, you can conclude that the parabola whose Leading Coefficient is closest to zero, must be the most compressed parabola of all the graphs.
Hence, the Leading Coefficient that is closest to zero is:
[tex]B[/tex]
(c) By definition, a negative number is less than a positive number.
Therefore, you conclude that the Leading Coefficient with the least value, in this case, must be negative.
Knowing that in this case, you have two parabolas with negative Leading Coefficients, you need to identify that one whose Absolute Value (its distance from zero) is the greatest one. In this case, this is the one that also produces the largest stretch of the parabola:
[tex]A[/tex]
Hence, the answers are:
