Fine the minimum value of y=f(x) and the corresponding value of x

Mathematics

ScanSolve AI Answer

Answer

-6.25
1.5

Step-by-step solution

3 steps

To find the minimum value of y=f(x)y=f(x) and the corresponding value of xx for the function f(x)=x2−3x−4f(x) = x^2 - 3x - 4:

  1. Identify the coefficients of the quadratic function.

    The function is in the form ax2+bx+cax^2 + bx + c, where a=1a=1, b=−3b=-3, and c=−4c=-4. Since a>0a > 0, the parabola opens upwards, and its vertex represents the minimum point.

  2. Calculate the x-coordinate of the vertex using the formula x=−b2ax = \frac{-b}{2a}.

    x=−(−3)2(1)x = \frac{-(-3)}{2(1)} x=32x = \frac{3}{2} x=1.5x = 1.5

  3. Substitute this x-value back into the function to find the minimum y-value.

    f(1.5)=(1.5)2−3(1.5)−4f(1.5) = (1.5)^2 - 3(1.5) - 4 f(1.5)=2.25−4.5−4f(1.5) = 2.25 - 4.5 - 4 f(1.5)=−2.25−4f(1.5) = -2.25 - 4 f(1.5)=−6.25f(1.5) = -6.25

    The minimum value of y=f(x)y=f(x) is −6.25\boxed{-6.25} and the corresponding value of xx is 1.5\boxed{1.5}.

    3 de faites, encore 2 aujourd'hui. Tu progresses.

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