To find the minimum value of the quadratic function f(x) = 16x^2 + 2x + 5, we can use the formula for the x-coordinate of the vertex of a parabola, which is -b/2a. In this case, a = 16 and b = 2.

Step 1: Calculate -b/2a
x = -2/(2*16) = -2/32 = -1/16

Step 2: Substitute x = -1/16 into the function to find the minimum value.
f(-1/16) = 16*(-1/16)^2 + 2*(-1/16) + 5 = 16/256 - 2/16 + 5 = 1/16 - 1/8 + 5 = 1/16 - 2/16 + 80/16 = 79/16

So, the minimum value of the function 16x^2 + 2x + 5 is 79/16 or approximately 4.9375.

Question

To find the minimum value of the quadratic function f(x) = 16x^2 + 2x + 5, we can use the formula for the x-coordinate of the vertex of a parabola, which is -b/2a. In this case, a = 16 and b = 2.

Step 1: Calculate -b/2a
x = -2/(2*16) = -2/32 = -1/16

Step 2: Substitute x = -1/16 into the function to find the minimum value.
f(-1/16) = 16*(-1/16)^2 + 2*(-1/16) + 5 = 16/256 - 2/16 + 5 = 1/16 - 1/8 + 5 = 1/16 - 2/16 + 80/16 = 79/16

So, the minimum value of the function 16x^2 + 2x + 5 is 79/16 or approximately 4.9375.

Knowee AI · Accepted Answer

To find the minimum value of the quadratic function f(x) = 16x^2 + 2x + 5, we can use the formula for the x-coordinate of the vertex of a parabola, which is -b/2a. In this case, a = 16 and b = 2.

Step 1: Calculate -b/2a
x = -2/(2*16) = -2/32 = -1/16

Step 2: Substitute x = -1/16 into the function to find the minimum value.
f(-1/16) = 16*(-1/16)^2 + 2*(-1/16) + 5 = 16/256 - 2/16 + 5 = 1/16 - 1/8 + 5 = 1/16 - 2/16 + 80/16 = 79/16

So, the minimum value of the function 16x^2 + 2x + 5 is 79/16 or approximately 4.9375.

Find the minimum value of 16𝑥2+2𝑥+5

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