To find the minimum value of a quadratic equation, we first need to know the general form of the quadratic equation, which is:
\[ y = ax^2 + bx + c \]
where \( a \), \( b \), and \( c \) are constants, and \( a \) is not equal to zero.
The minimum (or maximum) value of a quadratic function occurs at the vertex of the parabola. The x-coordinate of the vertex can be found using the formula:
\[ x = -\frac{b}{2a} \]
Once we find the x-coordinate of the vertex, we can substitute this value back into the equation to find the corresponding y-value, which will be the minimum value of the quadratic function if \( a > 0 \) (indicating that the parabola opens upwards).
To summarize the steps:
- Identify the coefficients \( a \), \( b \), and \( c \) from the quadratic equation.
- Calculate the x-coordinate of the vertex using \( x = -\frac{b}{2a} \).
- Substitute this x-value back into the original equation to find the minimum value of \( y \).
If you provide the specific quadratic equation, I can help you calculate the minimum value of \( y \).
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