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Answer:
Part a) The function’s equation written in vertex form is
Part b) The function’s equation written in factored form is equal to
Step-by-step explanation:
Part a) What is the function’s equation written in vertex form?
we know that
The equation of a vertical parabola written in vertex form is equal to
where
a is a coefficient
(h,k) is the vertex
Looking at the graph
The vertex is the point (2,-8)
substitute
Find the value of the coefficient a
take one point from the graph
(0,0)
substitute in the equation
therefore
The function’s equation written in vertex form is
Part b) What is the function’s equation written in factored form?
we know that
The equation of a vertical parabola written in factored form is equal to
where
a is a coefficient
x_1 and x_2 are the zeros or x-intercepts of the function
Remember that the x-intercept is the value of x when the value of the function is equal to zero
Looking at the graph
The zeros or x-intercepts of the function are
x=0 and x=4
so
Find the value of the coefficient a
take one point from the graph
(2,-8)
substitute
therefore
The function’s equation written in factored form is equal to