with quadratic functions how do you know if a parabola on a graph is supposed to open upwards or downwards?
ex. y=-4(x+1)2+4
[The 2 after the bracket is a square)
a parabola on a graph opens upwards if the "a" value in y=a(x+b)^2+c is positive. If "a" is negative, it opens downwards.
in the example it would open down, because the "a" value is negative
OHHHH !!!
okaay thanks !
To determine the direction in which a parabola opens based on a given quadratic function, you need to examine the coefficient of the squared term.
In the given example, the quadratic function is in the form of y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola. The coefficient "a" is what determines the direction of the parabola.
If the coefficient "a" is positive, the parabola opens upwards, and if "a" is negative, the parabola opens downwards.
Now, analyzing the given quadratic function y = -4(x + 1)^2 + 4, we see that the coefficient "a" is -4. Since -4 is negative, the parabola opens downwards.
Therefore, the graph of y = -4(x + 1)^2 + 4 will be a downward-opening parabola.