1. Find a formula for the quadratic function whose graph has a vertex of (-2,-3) and a y-intercept of -4.
2.Find the minimum and maximum value of the function y= -(x-2)^2+5.
-I know the minimum value is -infinity but I have no idea how to calculate the maximum value.
Thank you everyone!
2.Find the minimum and maximum value of the function y= -(x-2)^2+5.
-I know the minimum value is -infinity but I have no idea how to calculate the maximum value.
Thank you everyone!
-
Second problem:
II will do the second problem first, because that will help with the first one.
Notice that -(x-2)^2 <= 0. We get the maximum value when it equals 0, that is when x=2, which gives a maximum value of 5. (2,5) is the vertex of the parabola.
First problem:
Since (-2,-3) is the vertex, the form of the equation must be y = a(x+2)^2 -3 for some constant a. To find a, set y=4 and x=0. 4 = a(0+2)^2 -3. 4 = 4a - 3. a= 7/4
The equation then is 7/4(x+2)^2 - 3
II will do the second problem first, because that will help with the first one.
Notice that -(x-2)^2 <= 0. We get the maximum value when it equals 0, that is when x=2, which gives a maximum value of 5. (2,5) is the vertex of the parabola.
First problem:
Since (-2,-3) is the vertex, the form of the equation must be y = a(x+2)^2 -3 for some constant a. To find a, set y=4 and x=0. 4 = a(0+2)^2 -3. 4 = 4a - 3. a= 7/4
The equation then is 7/4(x+2)^2 - 3