To find the maximum or minimum value of the function, we can use the vertex formula. The vertex formula is given by x = -b/2a, where a, b, and c are the coefficients of the function.
In the given function, a = -2 and b = 32. Substituting these values into the vertex formula, we have x = -32/(2*(-2)) = -32/(-4) = 8.
To find the y-coordinate of the vertex, we substitute the value of x back into the function: y = -2(8)^2 + 32(8) - 12 = -128 + 256 - 12 = 116.
Therefore, the vertex of the function is (8, 116). Since the coefficient of x^2 is negative, the parabola opens downwards, meaning the vertex represents the maximum point of the function.
Hence, the maximum value of the function is 116.
To determine the range of the function, we consider the behavior of the parabola. Since the parabola opens downwards, the range will be all y-values less than or equal to the maximum value.
Therefore, the range of the function is y ≤ 116.
What is the maximum or minimum value of the function? What is the range?
y = –2x2 + 32x –12 (1 point)
1 answer