what is the range of f(x)=2x^2-4x-3 if the domain is [-3,3]? A)[-5,-27] B)-3,27 C)3,27 D)-5,27

Question

please help me with this question

Answer 1

Hi Rubie,

The range is a list of all y-values from the lowest to the highest.

A function with an x² like this will be a U-shaped parabola that will have its lowest y-value at the bottom. First we need to find what the x value would be at the bottom. The formula for this is -b / 2a, in this problem a = 2 (the value in front of the x²) and b = -4 (the value in front of the x). So the x-value would be -(-4) / 2(2) = 1. Now we can find the y-value by plugging x = 1 into the function: 2(1)² - 4(1) - 3 = -5. This is the lowest value in the range.

To find the highest value, we will plug in the two endpoints of the domain [-3, 3]:

x = -3: 2(-3)² - 4(-3) -3 = 27

x = 3: 2(3)² - 4(3) - 3 = 3

Since 27 is the highest, we now know the total range is [-5, 27] answer D.

Please let me know if I can be more helpful, thanks!

Joe