To find the maximum or minimum value of the function, we need to determine the vertex of the quadratic equation. The vertex can be found using the formula x = -b/2a.
In this case, a = -2 and b = 32.
x = -32/(2*(-2))
x = -32/(-4)
x = 8
To find the y-value of the vertex, we substitute the value of x into the equation:
y = -2(8)^2 + 32(8) - 12
y = -2(64) + 256 - 12
y = -128 + 256 - 12
y = 116
Therefore, the vertex is (8, 116).
Since the coefficient of the x^2 term is negative (-2), the parabola opens downwards and the vertex represents the maximum value of the function. Therefore, the maximum value of the function is 116.
The range of the function is all the possible values of y. Since the parabola opens downwards and the maximum value is 116, the range will be all real numbers less than or equal to 116.
What is the maximum or minimum value of the function? What is the range? y = –2x2 + 32x –12 :
116 range: y 116 maximum:
116 range: A symbol less than or equal to 116 maximum:
–116 range: y –116 maximum: –116 range: y Image with alt text: greater than equal to –116 maximum:
116 range: y 116 maximum: 116 range: y Image with alt text: greater than equal to
116 maximum: –116 range: y –11
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