Answer:
The function has a maximum
The function's maximum value is y = - 4
The maximum value occurs at x = 2
Step-by-step explanation:
The given function is
f(x) = - 2x^2 + 8x - 12
The leading coefficient(the coefficient of the term with the highest exponent, x^2) is - 2. Since the leading coefficient is negative, the parabola would open downwards. This means that it would have its highest point of vertex at the top. Thus,
the function has a maximum
Recall, the standard form of a quadratic equation is expressed as
y = ax^2 + bx + c
By comparing both equations,
a = - 2, b = 8, c = - 12
We would find the x coordinate of the maximum point by applying the formula,
x = - b/2a
By substituting the given values into the formula, we have
x = - 8/2 * - 2 = - 8/- 4
x = 2
We would find the y coordinate or maximum value by substituting x = 2 into
y = - 2x^2 + 8x - 12
y = - 2(2)^2 + 8(2) - 12
y = - 8 + 16 - 12
y = - 4
Thus,
the function's maximum value is y = - 4
The maximum value occurs at x = 2