Another Method for Finding the Vertex of a Quadratic Function

Another Method for finding the Vertex of a Quadratic Function

I. Complete the table below. Use your graphing calculator to find the vertex of each function.

Equation a b c Vertex y = 7x2 – 56x + 118 y = -2x2 – 4x – 13 y = 4x2 + 4.8x + 25.6 y = -0.2x2 – 0.2x – 10.6

Given what you see in the table, how can we find the x-coordinate of the vertex of ANY quadratic function in the form y = ax2 + bx + c?

Once you know the x-coordinate for any function, how can you find the y-coordinate of the point?

Write a two-step process to find the vertex of any quadratic function in the form y = ax2 + bx + c.

II. Challenge: We learned the quadratic formula in two different ways:

x = AND x = ±

Consider the second version and your conclusions in part I of this exploration. Why does it make sense that the two x- intercepts of quadratic function can be found by x = + AND x = -