Question

The graph of quadratic function f(x) has a minimum at (-2,- 3 and passes through the point (2, 13). The functio

g(x) is represented by the equation g(x)= -(x+2)(x-3)
How much greater is the y-intercept of g(x) than f(x)?

Answer 1

Explanation:

hello :

the vertex -form of quadratic function f(x) is : f(x) = a(x+b)²+c

the vertex : (- b , c )

means : (-2,-3) so : -b = -2 and c = - 3 so : b =2 and c = -3

f(x) = a(x+2)²-3

calculate : a

the graph passes through the point (2, 13) : f(2)=13

means : a(2+2)²-3 = 13

16a - = 13

16a = 16 so : a = 1

f(x) is represented by the equation f(x) = (x+2)²-3

The graph of f(x) color red and g(x) blue

is the y-intercept when g(x) greater g(x) than f(x) is when x=0 so : y = 6