Question

Write an equation of a quadratic function with a

minimum value of y = 2 and an axis of symmetry of
X=4

Answer 1

y = x² - 8x + 18

Explanation:

The minimum value occurs at the vertex, thus the y- coordinate of the vertex is 2

The axis of symmetry is vertical and passes through the vertex , thus the x- coordinate of the vertex is 4

The vertex of the quadratic is therefore (4, 2 )

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier.

let a = 1, then

y = (x - 4)² + 2 ← expand (x - 4)² using FOIL

= x² - 8x + 16 + 2

y = x² - 8x + 18 ← is a possible equation