Question

Find the vertex of the quadratic function

f(x) = 2x^2 - 6x + 7

A.) (0, 7)
B.) (1, 2)
C.) (-1.5, 2.5)
D.) (1.5, 2.5)

Answer 1

(1.5,2.5)

Explanation:

f(x) = 2x^2 - 6x + 7

Take the first derivative and set it equal to 0 (the slope is 0 at the vertex)

f'(x) = 4x -6

0 = 4x - 6

4x = 6

x = 3/2 or 1.5

If x = (3/2), then y = 2(3/2)^2 - 6(3/2) + 7

y = 2(9/4) - 18/2 + 7

y = (9/2) - 2

y = 2.5

See attached graph.