Question

The graph of quadric function has a minumum at (-2,-3) and passes through the point (2,13)

Answer 1

Answer:

g(x) = x² + 4x + 1

Step-by-step explanation:

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

Here (h, k) = (- 2, - 3), thus

y = a(x + 2)² - 3

To find a substitute (2, 13) into the equation

13 = a(2 + 2)² - 3

13 = 16a - 3 ( add 3 to both sides )

16 = 16a ( divide both sides by 16 )

a = 1, hence

g(x) = (x + 2)² - 3 ← expand factor and simplify

      = x² + 4x + 4 - 3

g(x) = x² + 4x + 1