Question

I need help with the answer

Answer 1

f(x)= x²(x+4)(x-3), g(x)= (x+2)²(x+6)(x-1)

Explanation:

you have the roots at -4,0, and 3

look at what the graph is doing at those points and see that

-at -4 and at 3 the graph crosses the x-axis so in the equation you will have (x-root)

-at 0 the graph is touching the x-axis and then goes back above/under it so in the equation you will have (x-root)²

f(x)= x²(x+4)(x-3)

g(x) left 2 units

when you move a function to the left/ right you add/subtract that amount to the value of x so

g(x)= (x+2)²(x+2+4)(x+2-3)

g(x)= (x+2)²(x+6)(x-1)

Answer 2

Hi there!

Looking at the graph, we can see zeroes at x = -4, 0 (bounce, degree of 2) and 3. The graph is also face up, so it is positive. We can write an equation in factored form:

f(x) = x²(x + 4)(x - 3)

Find the equation of g by translating each zero left. The new zeros would be:

x = -6, x = -2, and x = 1

Write the polynomial:

g(x) = (x + 2)²(x + 6)(x - 1)