Question
Find the minimum value of the function to the nearest hundredth
f(x) = 2x^2 - 4x + 5
f(x) = 2x^2 - 4x + 5
Answers
GPT 3.5
To find the minimum value of the function f(x) = 2x^2 - 4x + 5, we can use the formula for the x-coordinate of the vertex, which is given by x = -b/2a.
In this case, a = 2 and b = -4. Plugging these values into the formula, we get:
x = -(-4) / (2*2) = 4 / 4 = 1
To find the y-coordinate of the vertex, we substitute x = 1 into the equation f(x):
f(1) = 2(1)^2 - 4(1) + 5
= 2(1) - 4 + 5
= 2 - 4 + 5
= 3
Therefore, the minimum value of the function is 3, rounded to the nearest hundredth.
In this case, a = 2 and b = -4. Plugging these values into the formula, we get:
x = -(-4) / (2*2) = 4 / 4 = 1
To find the y-coordinate of the vertex, we substitute x = 1 into the equation f(x):
f(1) = 2(1)^2 - 4(1) + 5
= 2(1) - 4 + 5
= 2 - 4 + 5
= 3
Therefore, the minimum value of the function is 3, rounded to the nearest hundredth.