Question

f(x) = −16x2 + 22x + 3
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points)

Answer 1

You *could* solve this by graphing, but they are most likely expecting an algebraic solution.

Is the vertex of the graph of f(x) going to be a maximum or a minimum? ---> check the sign of the leading coefficient. if it's positive, then the parabola will point upwards and you'll have a minimum. if negative, the parabola will point downwards and you'll have a maximum. see which one of these statements applies to f(x)

What are the coordinates of the vertex? Justify your answers and show your work. ---> take the b coefficient (your x term is 22x so your b coefficient is simply 22). calculate (-b/2a) as your x-coordinate, plug this x-value into the function to get the corresponding y-value.