Questions: Determine whether (f(x)=2 x^2+4 x-8) has a minimum or maximum value, and find the value of the minimum or maximum. Also, find the axis of symmetry. The value of the square is square help (numbers) The axis of symmetry for (f(x)) is given by square

Solution Steps

To determine whether the quadratic function \( f(x) = 2x^2 + 4x - 8 \) has a minimum or maximum value, we need to look at the coefficient of \( x^2 \). Since it is positive, the parabola opens upwards, indicating a minimum value. The minimum value occurs at the vertex of the parabola. The axis of symmetry can be found using the formula \( x = -\frac{b}{2a} \).

The axis of symmetry for the quadratic function \( f(x) = 2x^2 + 4x - 8 \) is calculated using the formula:

\[ x = -\frac{b}{2a} \]

Substituting the values \( a = 2 \) and \( b = 4 \):

\[ x = -\frac{4}{2 \cdot 2} = -1.0 \]

The minimum value of the function occurs at the vertex, which can be found by evaluating \( f(x) \) at the axis of symmetry \( x = -1.0 \):

\[ f(-1.0) = 2(-1.0)^2 + 4(-1.0) - 8 \]

Calculating this gives:

\[ f(-1.0) = 2(1) - 4 - 8 = 2 - 4 - 8 = -10.0 \]

Final Answer