To find the maximum or minimum value of the function, we can use the formula -b/2a for the x-coordinate of the vertex of a quadratic function in the form ax^2 + bx + c.
For y = -2x^2 + 32x - 12, the coefficient of x^2 is -2, the coefficient of x is 32, and the constant term is -12.
By substituting these values into the formula -b/2a, we get:
x = -32 / (2 * -2)
x = -32 / -4
x = 8
To find the y-coordinate of the vertex, we substitute the x-coordinate into the function:
y = -2(8)^2 + 32(8) - 12
y = -2(64) + 256 - 12
y = -128 + 256 - 12
y = 116
The maximum value of the function is therefore 116.
To find the range, we consider that a quadratic function with a negative coefficient of x^2 opens downwards and has a vertex at the maximum value.
So, the range of y = -2x^2 + 32x - 12 is y ≤ 116.
What is the maximum or minimum value of the function? What is the range? y = –2x2 + 32x –12 (1 point) Responses maximum: 116 range: y 116 maximum: 116 range: y Image with alt text: 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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