Question

Jen knows that (-1, 41) and (5, 41) lie on a parabola defined by the equation y=4x^2-16x+21. How can I find the coordinates of the vertex?

Answer 1

The vertex is at (2, 5).

To find the vertex, we first find the axis of symmetry; this is given by

x = -b/2a

For our equation, b = -16 and a = 4:
x = -(-16)/2(4) = 16/8 = 2

We substitute this back into our equation:
y = 4(2)² - 16(2) + 21 = 4(4) - 32 + 21 = 5

Therefore the vertex is at (2, 5).