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Answer the questions below about the quadratic function. f(x) = - 2x ^ 2 + 8x - 12

Answer the questions below about the quadratic function. f(x) = - 2x ^ 2 + 8x - 12-example-1

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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

User Ferdous Ahamed
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