The graph of a quadratic function has a y intercept at (0,5) and minimum at (3, -4), write the equation of its curve

Question

the graph of a quadratic function has a y intercept at (0,5) and minimum at (3, -4),

 

Question a: write the equation of its curve

Question b: write the coordinates of the root of this quadratic function

Answer 1

(a)

The minimum is the vertex, and it opens upward.

y = a(x - h)² + k,

where a > 0.

h = 3

y = -4

y = a(x - 3)² - 4

5 = a(0 - 3)² - 4

5 = 9a - 4

a = 1

y = (x - 3)² - 4

(b)

(x - 3)² - 4 = 0

x - 3 = ±2

x = 5 or 1

The roots are at (5,0) and (1,0).