Final answer:
The axis of symmetry for the quadratic function f(x) = 4x² - 2x - 3 is x = 1/4, calculated using the formula x = -b/(2a).
Step-by-step explanation:
The axis of symmetry for a quadratic function, such as f(x) = 4x² - 2x - 3, can be determined using the formula x = -b/(2a). This is derived from the general form of a quadratic equation, ax² + bx + c = 0. For the function in question, 'a' is 4 and 'b' is -2.
Step-by-step solution:
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- Identify the coefficients 'a' and 'b': In our case, 'a' = 4 and 'b' = -2.
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- Apply the formula for the axis of symmetry: x = -b/(2a)
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- Calculate the value: x = -(-2)/(2*4) = 2/8 = 1/4.
Therefore, the axis of symmetry for the function f(x) = 4x² - 2x - 3 is x = 1/4.