Questions: Find the vertex. f(x)=x^2+3x+4 (-3/2, [?]/)

Solution Steps

To find the vertex of a quadratic function in the form \( f(x) = ax^2 + bx + c \), we use the vertex formula \( x = -\frac{b}{2a} \) to find the x-coordinate of the vertex. Then, we substitute this x-coordinate back into the function to find the corresponding y-coordinate.

Given the quadratic function \( f(x) = x^2 + 3x + 4 \), we identify the coefficients:

• \( a = 1 \)
• \( b = 3 \)
• \( c = 4 \)

The x-coordinate of the vertex for a quadratic function \( f(x) = ax^2 + bx + c \) is given by: \[ x = -\frac{b}{2a} \] Substituting the values of \( a \) and \( b \): \[ x = -\frac{3}{2 \cdot 1} = -\frac{3}{2} = -1.5 \]

To find the y-coordinate, substitute \( x = -1.5 \) back into the function \( f(x) \): \[ f(-1.5) = (1)(-1.5)^2 + (3)(-1.5) + 4 \] \[ = 2.25 - 4.5 + 4 \] \[ = 1.75 \]

Final Answer