Questions: Determine the vertex of the graph of the following parabola. f(x) = x^2 - 30x + 3

Solution Steps

To find the vertex of a parabola given by the equation \( f(x) = ax^2 + bx + c \), we can use the vertex formula \( x = -\frac{b}{2a} \). Once we have the x-coordinate of the vertex, we can substitute it back into the equation to find the y-coordinate.

Given the quadratic function \( f(x) = x^2 - 30x + 3 \), we identify the coefficients:

• \( a = 1 \)
• \( b = -30 \)
• \( c = 3 \)

The x-coordinate of the vertex of a parabola \( f(x) = ax^2 + bx + c \) is given by: \[ x = -\frac{b}{2a} \] Substituting the values of \( a \) and \( b \): \[ x = -\frac{-30}{2 \cdot 1} = \frac{30}{2} = 15.0 \]

To find the y-coordinate, substitute \( x = 15.0 \) back into the function \( f(x) \): \[ y = f(15.0) = 1 \cdot (15.0)^2 - 30 \cdot 15.0 + 3 \] \[ y = 225.0 - 450.0 + 3 = -222.0 \]

Final Answer