Find the maximum or minimum value of \( f(x)=-3 x^{2}+30 x+8 \) The select an answer \( \odot \) is

To find the maximum or minimum of the quadratic function \( f(x) = -3x^2 + 30x + 8 \), we can use the vertex formula. The x-coordinate of the vertex is given by \( x = -\frac{b}{2a} \). Here, \( a = -3 \) and \( b = 30 \). Calculating the x-coordinate gives: \( x = -\frac{30}{2 \cdot -3} = 5 \). Now substitute \( x = 5 \) back into the function: \( f(5) = -3(5^2) + 30(5) + 8 = -75 + 150 + 8 = 83 \). So, the maximum value of the function is \( 83 \) when \( x = 5 \). The select an answer \( \odot \) is \( 83 \). If you have a quadratic function where \( a < 0 \), you will always find a maximum value at the vertex because the parabola opens downwards. For our function, the peak forms a cozy little mountain, with all points below it. Always look for that vertex when you're dealing with parabolas! When dealing with quadratic equations, it’s essential to sketch them or visualize where their vertex lies—often, students forget to consider how the sign of \( a \) (in \( ax^2 + bx + c \)) affects whether the graph opens up or down. Remember, a simple sign change can turn a maximum into a minimum and vice versa!