Fill in the Blank 4 points Given the equation to the right, f(x)=2x^2+8x+3 a) What is the vertex? ( square square 2 4 :-2 :-5 &3 i maximum if minimum

To find the vertex of the quadratic function \( f(x) = 2x^2 + 8x + 3 \), we can use the vertex formula for a parabola given by \( y = ax^2 + bx + c \). The x-coordinate of the vertex is found using the formula:<br /><br />\[ x = -\frac{b}{2a} \]<br /><br />In this equation, \( a = 2 \) and \( b = 8 \).<br /><br />Substitute these values into the formula:<br /><br />\[ x = -\frac{8}{2 \times 2} = -\frac{8}{4} = -2 \]<br /><br />Now, substitute \( x = -2 \) back into the original equation to find the y-coordinate of the vertex:<br /><br />\[ f(-2) = 2(-2)^2 + 8(-2) + 3 \]<br />\[ f(-2) = 2(4) - 16 + 3 \]<br />\[ f(-2) = 8 - 16 + 3 \]<br />\[ f(-2) = -5 \]<br /><br />Therefore, the vertex of the parabola is \((-2, -5)\).<br /><br />Since the coefficient of \( x^2 \) (which is 2) is positive, the parabola opens upwards, indicating that the vertex is a minimum point.<br /><br />So, the answers are:<br />a) The vertex is \((-2, -5)\).<br />b) The vertex is a minimum.